ńņš. 18 |

the scope of this chapter.

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 455

purposes of a fairness opinion. If a bank loans $10 million to the ESOP

for a 100% sale, with no recourse or personal guarantees of the owner,

we may likely decide it is not a fair transaction to the ESOP and its

participants. We would have serious questions about the ESOPā™s proba-

bility of becoming a long-range retirement program, given the huge debt

load of the Company post-transaction.

Charity

While the dilution technically belongs to the ESOP, I consider it my duty

to inform the seller of the dilution phenomenon and how it works. While

afļ¬rming the sellerā™s right to receive fair market value undiminished by

dilution, I do mention that if the seller has any charitable motivations to

his or her employeesā”which a minority doā”then voluntarily accepting

some of the dilution will leave the Company and the ESOP in better

shape. Of course, in a partial sale it also leaves the remainder of the

ownerā™s stock at a higher value than it would have had with the ESOP

bearing all of the dilution.

BIBLIOGRAPHY

Abrams, Jay B. 1993. ā˜ā˜An Iterative Procedure to Value Leveraged ESOPs.ā™ā™ Valuation (Jan-

uary): 71ā“103.

ā” ā”. 1997. ā˜ā˜ESOPs: Measuring and Apportioning Dilution.ā™ā™ Valuation (June): 3ā“25.

ā”

Miller, Merton, and Franco Modigliani. 1958. ā˜ā˜The Cost of Capital, Corporation Finance,

and the Theory of Investment.ā™ā™ American Economic Review 48: 61ā“97.

APPENDIX A: MATHEMATICAL APPENDIX

The purpose of this appendix is to perform comparative static analysis,

as is commonly done in economics, on the equations for dilution in the

body of the chapter in order to understand the tradeoffs between type 1

and type 2 dilution.

We use the same deļ¬nitions in the appendix as in the chapter. Type

1 dilution is equal to the payment to the owner less the post-transaction

value of the ESOP, or x (13-3f):

D1 x [pDE(1 e) (1 t)pDEx] (A13-1)

Factoring out the x,

D1 x[1 (1 t)pDE] pDE(1 e) (A13-2)

We can investigate the impact on type 1 dilution for each $1 change

in payment to the owner by taking the partial derivative of (A13-2) with

respect to x.

D1

1 (1 t)pDE 1 (A13-3)

x

Equation (A13-3) tells us that each additional dollar paid to the owner

increases dilution to the ESOP by more than $1.

A full payment to the owner (the default payment) is pDE for $1 of

pre-transaction value. We pay the owner x, and the difference of the two

is D2, the type 2 dilution.

PART 5 Special Topics

456

D2 pDE x (A13-4)

We can investigate the impact on type 2 for each $1 change in payment

to the owner by taking the partial derivative of (A13-4) with respect

to x.

D2

1 (A13-5)

x

Type 2 dilution moves in an equal but opposite direction from the amount

paid to the owner, which must be the case to make any sense. Together,

equations (A13-3) and (A13-5) tell us that each additional dollar paid the

owner increases the dilution to the ESOP more than it reduces the dilution

to the owner. We can also see this by taking the absolute value of the

ratio of the partial derivatives:

D2/ x 1

1 (A13-6)

D1/ x 1 (1 t)pDE

Signiļ¬cance of the Results

Equation (A13-6) demonstrates that for every $1 of payment forgone by

the owner, the dilution incurred by the owner will always be less than

the dilution eliminated to the ESOP. The reason for this is that every $1

the owner forgoes in payment costs him $1 in type 2 dilution, yet it saves

the ESOP:

1. The $1, plus

2. It reduces the ESOP loan by pDE and saves the ESOP the after-

tax cost of the lowered amount of the loan, or (1 t)pDE.

There appears to be some charity factor inherent in the mathematics.

Finally, we have not dealt with the fact that by the owner taking on

some or all of the dilution from the ESOP loan, he or she increases the

value of his or her (1 p) share of the remaining stock by reducing the

dilution to it. Such an analysis has no impact on the valuation of the

ESOP, but it should be considered in the decision to initiate an ESOP.

APPENDIX B: SHORTER VERSION OF CHAPTER 13

This appendix provides a bare-bones version of Chapter 13, removing all

mathematical analysis and optional sections of the iterative approach and

all of the second part of the chapter. The reader can then see the bottom

line of the chapter without struggling through the voluminous mathe-

matics. It will also serve as a refresher for those who have already read

the chapter.

INTRODUCTION

Leveraged ESOPs have confused many ļ¬rms due to their failure to un-

derstand the phenomenon of dilution and inability to quantify it. Many

ESOPs have soured because employees paid appraised fair market value

of the stock being sold to the ESOP, only to watch the fair market value

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 457

signiļ¬cantly decline at the next valuation because the ESOP loan was not

included in the pre-transaction fair market value. As a result, employees

have felt cheated. Lawsuits have sometimes followed, further lowering

the value of the ļ¬rm and the ESOP.

There are several types of problems relating to the dilution phenom-

enon:

1. The technical problem of deļ¬ning and measuring the dilution in

value to the ESOP before it happens.

2. The business problem of getting the ESOP Trustee, participants,

and selling owner(s) to agree on how to share the dilution.

3. The technical problem of how to engineer the price to

accomplish the desired goals in 2.

4. The problem of how to communicate each of the foregoing to all

of the participants so that all parties can enter the transaction

with both eyes open and come away feeling the transaction was

winā“win instead of winā“lose.

This chapter provides the analytical solutions to problems 1 and 3

that are necessary for resolving the business and communication prob-

lems of 2 and 4. The appraiser will be able to include the dilution in his

or her initial valuation report so that employees will not be negatively

surprised when the value drops at the next annual valuation. Addition-

ally, the appraiser can provide the technical expertise to enable the parties

to share the dilution, solving problem 3. Both parties will then be fully

informed beforehand, facilitating a winā“win transaction.

DEFINITIONS OF DILUTION

Two potential parties can experience dilution in stock values in ESOP

transactions: the ESOP and the owner. The dilution that each experiences

differs and can be easily confused.

Additionally, each party can experience two types of dilution: abso-

lute and relative. Absolute dilution is deļ¬ned in the section immediately

below. Relative dilution is more complicated because we can calculate

dilution relative to more than one base. Several formulas can be devel-

oped to calculate relative dilution, but they are beyond the scope of this

book. Thus, for the remainder of this chapter, dilution will mean absolute

dilution.

Dilution to the ESOP (Type 1 Dilution)

We deļ¬ne type 1 dilution as the payment to the selling owner less the

post-transaction fair market value of the ESOP. This can be stated either

in dollars or as a percentage of the pre-transaction value of the ļ¬rm. By

law, the ESOP may not pay more than fair market value to the company

or to a large shareholder, though it is nowhere deļ¬ned in the applicable

statute whether this is pre- or post-transaction value. Case law and De-

PART 5 Special Topics

458

partment of Labor proposed regulations indicate that the pre-transaction

value should be used.23

Dilution to the Selling Owner (Type 2 Dilution)

We deļ¬ne Type 2 dilution as the difference in the pre-transaction fair

market value of the shares sold and the price paid to the seller. Again,

this can be in dollars or as a percentage of the ļ¬rmā™s pre-transaction value.

Since it is standard industry practice for the ESOP to pay the owner the

pre-transaction price, Type 2 Dilution is virtually unknown. Those sellers

who wish to reduce or eliminate dilution to the ESOP can choose to sell

for less than the pre-transaction fair market value.

When the ESOP bears all of the dilution, we have only type 1 dilu-

tion. When the owner removes all dilution from the ESOP by absorbing

it himself, then the selling price and post-transaction values are equal and

we have only type 2 dilution. If the owner absorbs only part of the di-

lution from the ESOP, then the dilution is shared, and we have both type

1 and type 2 dilution.

As we will show in Table 13-3B and the Mathematical Appendix,

when the seller takes on a speciļ¬c level of type 2 dilution, the decrease

in type 1 dilution is greater than the corresponding increase in type 2

dilution.

The seller also should consider the effects of dilution on his or her

remaining stock in the ļ¬rm, but that is beyond the scope of this book.

Deļ¬ning Terms

We ļ¬rst deļ¬ne some of terms appearing in the various equations.

Let:

p percentage of ļ¬rm sold to the ESOP, assumed at 30%

t combined federal and state corporate income tax rate, assumed

at 40%

r the annual loan interest rate, assumed at 10%

i the monthly loan interest rate r/12 0.8333% monthly

E the lifetime costs of initiating and running the ESOP. These

are generally legal fees, appraisal fees, ESOP administration fees,

and internal administration costs. We assume initial costs of

$20,000 and annual costs of $10,000 growing at 6% each year. Table

13-1 shows a sample calculation of the lifetime costs of the ESOP

as $40,000.24

e lifetime ESOP costs as a percentage of the pre-transaction

value E/V1B $40,000/$1 million 4%.

DE one minus net Discounts (or plus net premiums) at the ESOP

level. This factor converts the fair market value of the entire ļ¬rm

23. Donovan v. Cunningham, 716 F.2d 1467. 29 CFR 2510.3-18(b).

24. How to calculate the pre-transaction value of the ļ¬rm is outside the scope of this article.

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 459

on an illiquid control level (V1B) to a fair market value (on a 100%

basis) at the ESOPā™s level of marketability and control (DEV1B). If

we assume that the ESOP provides complete marketability (which

normally one should not, but we are doing so here for didactic

purposes), then to calculate DE we must merely reverse out the

control premium that was applied to the entire ļ¬rm (in the

calculation of V1B), which we will assume was 43%, and reverse

out the discount for lack of marketability that was applied, which

we will assume was 29%.25 The result is: DE [1/(1 43%)]

[1/(1 29%)] 0.7 1.4 0.98. In other words, the net effect of

reversing out the assumed discount and premium is a 2% net

discount. It could also be a net premium if the minority discount

were less or the premium for marketability were higher. Also, if

we were to assume that the ESOP shares were not at a marketable

minority level, other adjustments would be required.

D1 type 1 dilution (dilution to the ESOP)

D2 type 2 dilution (dilution to the seller)

FMV fair market value

TABLE 13-1: CALCULATION OF LIFETIME ESOP COSTS

We begin by calculating the lifetime cost of the ESOP, including the legal,

appraisal, and administration costs, which are collectively referred to

throughout this chapter as the administration costs or as the lifetime

ESOP costs.

The estimated annual operating costs of the ESOP in Table 13-1 are

$10,000 pretax (B5), or $6,000 after-tax (B6). We assume an annual re-

quired rate of return of 25% (B7). Letā™s further assume ESOP administra-

tion costs will rise by 5% a year (B8). We can then calculate the lifetime

value of the annual cost by multiplying the ļ¬rst yearā™s cost by a Gordon

model multiple (GM) using an end-of-year assumption. The GM formula

is 1/(r g), or 1/(0.25 0.05) 5.000 (B9). Multiplying 5.000 by $6,000,

we obtain a value of $30,000 (B10).

We next calculate the immediate costs of initiating the ESOP at time

zero, which we will assume are $20,000 (B11), or $12,000 after-tax (B12).

Adding $30,000 plus 12,000, we arrive at a lifetime cost of $42,000 for

running the ESOP (B13), which for simplicity we round off to $40,000

(B14), or 4% of the pre-transaction value of $1 million.26 Adopting the

previous deļ¬nitions, E $40,000 and e 4%.

The previous example presumes that the ESOP is not replacing an-

other pension plan. If the ESOP is replacing another pension plan, then

it is only the incremental lifetime cost of the ESOP that we would cal-

culate here.

25. These are arbitrary assumptions chosen for mathematical ease.

26. For simplicity, we do not add a control premium and deduct a discount for lack of

marketability at the ļ¬rm level and then reverse that procedure at the ESOP level, as I did in

Abrams (1993).

PART 5 Special Topics

460

THE DIRECT APPROACH

Using the direct approach, we calculate all valuation formulas directly

through algebraic substitution. We will develop post-transaction valua-

tion formulas for the following situations:

1. All dilution remains with the ESOP.

2. All dilution goes to the owner.

3. The ESOP and the owner share the dilution.

We will begin with 1. The owner will be paid pre-transaction price, leav-

ing the ESOP with all of the dilution in value. The following series of

equations will enable us to quantify the dilution. All values are stated as

a fraction of each $1 of pre-transaction value.

FMV Equationsā”All Dilution to the ESOP

(Type 1 Dilution; No Type 2 Dilution)

1 pre-transaction value (A13-7)

We pay the owner the p% he or she sells to the ESOP reduced or increased

by DE, the net discounts or premiums at the ESOP level. For every $1 of

pre-transaction value, the payment to the owner is thus:

pDE paid to owner in cash ESOP loan (A13-7a)

tpDE tax savings on ESOP loan (A13-7b)

The after-tax cost of the loan is the amount paid to the owner less the tax

savings of the loan, or equations (A13-7a) and (A13-7b).

(1 t)pDE after-tax cost of the ESOP loan (A13-7c)

e after-tax lifetime cost of the ESOP (A13-7d)

When we subtract (A13-7c) plus (A13-7d) from (A13-7), we obtain

the remaining value of the ļ¬rm:

1 (1 t)pDE e post-transaction value of the firm (A13-7e)

Since the ESOP owns p% of the ļ¬rm, the post-transaction value of the

ESOP is p DE (A13-7e):

t)p 2D2

pDE (1 pDE e

E

post-transaction value of the ESOP (A13-7f)

The dilution to the ESOP (type 1 dilution) is the amount paid to

the owner minus the value of the ESOPā™s p% of the ļ¬rm, or (A13-7a)

(A13-7f):

t)p 2D2

pDE [pDE (1 pDE e]

E

t)p 2D2

(1 pDE e dilution to ESOP (A13-7g)

E

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 461

Table 13-2, Sections 1 and 2: Post-transaction FMV with

All Dilution to the ESOP

Now that we have established the formulas for calculating the FMV of

the ļ¬rm when all dilution goes to the ESOP, letā™s look at a concrete ex-

ample in Table 13-2. The table consists of three sections. Section 1, rows

5ā“10, is the operating parameters of the model. Section 2 shows the cal-

culation of the post-transaction values of the ļ¬rm, ESOP, and the dilution

to the ESOP according to equations (A13-7e), (A13-7f), and (A13-7g), re-

spectively, in rows 12ā“18. Rows 21ā“26 prove the accuracy of the results,

as explained below.

Section 3 shows the calculation of the post-transaction values of the

ļ¬rm and the ESOP when there is no dilution to the ESOP. We will cover

that part of the table later. In the meantime, letā™s review the numerical

example in section 2.

B13 contains the results of applying equation (A13-7e) using section

1 parameters to calculate the post-transaction value of the ļ¬rm, which is

$0.783600 per $1 of pre-transaction value. We multiply the $0.783600 by

the $1 million pre-transaction value (B5) to calculate the post-transaction

value of the ļ¬rm $783,100 (B14). The post-transaction value of the ESOP

according to equation (A13-7f) is $0.23037827 (B15) $1 million pre-

transaction value (B5) $230,378 (B16).

We calculate dilution to the ESOP according to equation (A13-7g) as

0.32 0.982

(1 0.4) 0.3 0.98 0.04 0.063622 (B17). When we

multiply the dilution as a percentage by the pre-transaction value of $1

million, we get dilution of $63,622 (B18, B26).

We now prove these results and the formulas in rows 21ā“26. The

payment to the owner is $1 million 30% 0.98 (net of ESOP discounts/

premiums) $294,000 (B22). The ESOP takes out a $294,000 loan to pay

the owner, which the company will have to pay. The after-tax cost of the

loan is (1 t) multiplied by the amount of the loan, or 0.6 $294,000

$176,400 (B23). Subtracting the after tax cost of the loan and the $40,000

lifetime ESOP costs from the pre-transaction value, we come to a post-

transaction value of the ļ¬rm of $783,600 (B24), which is identical to the

value obtained by direct calculation using formula (A13-7e) in B14. The

post-transaction value of the ESOP is pDE post-transaction FMVā”ļ¬rm,

or 0.3 0.98 $783,600 $230,378 (B25, B16). The dilution to the ESOP

is the payment to the owner minus the post-transaction value of the ESOP,

or $294,000 (B22) $230,378 (B25) $63,622 (B26, B18). We have now

proved the direct calculations in rows 14, 16, and 18.

The Post-transaction Value Is a Parabola

Equation (A13-7f), the formula for the post-transaction value of the ESOP,

is a parabola. We can see this more easily by rewriting (A13-7f) as

D 2 (1 t)p 2

V DE(1 e)p

E

where V is the post-transaction value of the ESOP. Figure 13-1 shows this

27. Which itself is equal to pDE the post-transaction value of the ļ¬rm, or B6 B7 B14.

PART 5 Special Topics

462

(1 e) (1 t)x post-transaction value of the firm (A13-8e)

Since the ESOP owns p% of the ļ¬rm and the ESOP bears its net

discount, the post-transaction value of the ESOP is p DEx (A13-8e), or:

pDE(1 e) (1 t)pDEx

post-transaction value of the ESOP (A13-8f)

We can eliminate dilution to the ESOP entirely by specifying that the

payment to the owner, x, equals the post-transaction value of the ESOP

(A13-8f), or:

x pDE(1 e) (1 t)pDEx (A13-8g)

which solves to:

pDE (1 e)

x

1 (1 t)pDE

post-transaction FMV of ESOP, all dilution to owner (A13-8j)

Substituting equation (A13-8j) into the x term in equation (A13-8e), the

post-transaction value of the ļ¬rm is:

1 e

post-transaction value of the firmā”

1 (1 t)pDE

type 1 dilution 0 (A13-8n)

The dilution to the seller is the pre-transaction FMV of shares sold minus

the price paid, or:

1 e

pDE (A13-8o)

1 (1 t)pDE

Table 13-2, Section 3: FMV Calculationsā”All Dilution to

the Seller

In section 3 we quantify the engineered price that eliminates all dilution

to the ESOP, which according to equation (A13-8n) is:

(1 0.04)

$1 million

[1 (0.6) (0.3) (0.98)]

$1 million 0.816049 (B29) $816,049 (C29)

Similarly, the value of the ESOP is: 0.3 0.98 0.816049 $1,000,000

$239,918 (C30) which is also the same amount that the owner is paid

in cash. We can prove this correct as follows:

1. The ESOP borrows $239,918 (B37) to pay the owner and takes

out a loan for the same amount, which the ļ¬rm pays.

2. The ļ¬rm gets a tax deduction, which has a net present value of

its marginal tax rate multiplied by the principal of the ESOP

loan, or 40% $239,918, or $95,967 (B38), which after being

subtracted from the payment to the owner leaves an after-tax

PART 5 Special Topics

464

cost of the payment to the owner (which is identical to the after-

tax cost of the ESOP loan) of $143,951 (B39).

3. We subtract the after-tax cost of the ESOP loan of $143,951 and

the $40,000 lifetime ESOP costs from the pre-transaction value of

$1 million to arrive at the ļ¬nal value of the ļ¬rm of $816,049

(B40). This is the same result as the direct calculation by formula

in B29, which proves (A13-8n). Multiplying by pDE (0.3 0.98

0.297) would lead to the same result as in B30, which proves the

accuracy of (A13-8j).

We can also prove the dilution formulas in section 3. The seller ex-

periences dilution equal to the normative price he or she would have

received if he or she were not willing to reduce the sales price, i.e.,

$294,000 (B22) less the engineered selling price of $239,918 (C30), or

$54,082 (C33). This is the same result as using a direct calculation from

equation (A13-8o) of 5.4082% (C31) the pre-transaction price of $1 mil-

lion $54,082 (C32).

The net result of this approach is that the owner has shifted the entire

dilution from the ESOP to himself. Thus, the ESOP no longer experiences

any dilution in value. While this action is very noble on the part of the

owner, in reality few owners are willing and able to do so.

Sharing the Dilution

The direct approach also allows us to address the question of how to

share the dilution. If the owner does not wish to place all the dilution on

the ESOP or absorb it personally, he or she can assign a portion to both

parties. By subtracting the post-transaction value of the ESOP (A13-8f)

from the cash to the owner (A13-8a), we obtain the amount of dilution.

We can then specify that this dilution should be equal to a fraction k of

the default dilution, i.e., the dilution to the ESOP when the ESOP bears

all of the dilution. In our nomenclature, the post-transaction value of the

ESOP dilution to the ESOP k (default dilution to the ESOP). There-

fore,

Actual Dilution to ESOP

k ,

Default Dilution to ESOP

or k the % dilution remaining with the ESOP

The reduction in dilution to the ESOP is (1 k). For example, if k

33%, the ESOP bears 33% of the dilution; the reduction in the amount of

dilution borne by ESOP is 67% (from the default ļ¬gure of 100%).

The formula used to calculate the payment to the owner when di-

lution is shared by both parties is:

t)p 2 D 2

x [pDE(1 e) (1 t)pDEx] k[(1 pDE e] (A13-9)

E

which solves to:

t)p 2 D 2

pDE(1 e) k[(1 pDE e]

E

x (A13-9a)

1 (1 t)pDE

In other words, equation (A13-8a) is the formula for the amount of

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 465

payment to the owner when the ESOP retains the fraction k of the default

dilution. If we let k 0, (A13-8a) reduces to (A13-8j), the post-transaction

FMV of the ESOP when all dilution goes to the owner. When k 1, (A13-

9a) reduces to (A13-7a), the payment to the owner when all dilution goes

to the ESOP.

Equation to Calculate Type 2 Dilution

Type 2 dilution is equal to pDE, the pre-transaction selling price adjusted

for control and marketability, minus the engineered selling price, x. Sub-

stituting equation (A13-9a) for x, we get:

t)p 2 D E

2

pDE(1 e) k[(1 pDE e]

D2 pDE (A13-9b)

1 (1 t)pDE

Tables 13-3 and 13-3A: Adjusting Dilution to

Desired Levels

Table 13-3 is a numerical example using equation (A13-9a). We let p

30% (B5), DE 98% (B6), k 2/3 (B7), t 40% (B8), and e 4% (B9).

B10 is the calculation of x, the payment to the sellerā”as in equation (A13-

9a)ā”which is 27.6%. B11 is the value of the ESOP post-transaction, which

we calculate according to equation (A13-8f),30 at 23.36%. Subtracting the

post-transaction value of the ESOP from the payment to the owner

(27.60% 23.36%) 4.24% (B12) gives us the amount of type 1 dilution.

The default type 1 dilution, where the ESOP bears all of the dilution,

t)p2D 2

would be (1 pDEe, according to equation (A13-7g), or 6.36%

E

(B13). Finally, we calculate the actual dilution divided by the default di-

lution, or 4.24%/6.36% to arrive at a ratio of 66.67% (B14), or 2/3, which

is the same as k, which proves the accuracy of equation (A13-9a). By

designating the desired level of dilution to be 2/3 of the original dilution,

we have reduced the dilution by 1/3, or (1 k).

If we desire dilution to the ESOP to be zero, then we substitute k

0 in equation (A13-9a), and the equation reduces to

pDE(1 e)

x

[1 (1 t)pDE]

which is identical to equation (A13-8j), the post-transaction value of the

ESOP when the owner bears all of the dilution. You can see that in Table

13-3A, which is identical to Table 13-3 except that we have let k 0 (B7),

which leads to the zero dilution, as seen in B14.

Type 2 dilution appears in Table 13-3, rows 15 and 16. The owner is

paid 27.6% (B10) of the pre-transaction value for 30% of the stock of the

company. He normally would have been paid 29.4% of the pre-transaction

value (B5 B6 0.3 0.98 29.4%). Type 2 dilution is 29.4% 27.60%

1.80% (B15). In B16 we calculate type 2 dilution directly using equation

30. With pDE factored out.

PART 5 Special Topics

466

(A13-9b). Both calculations produce identical results, conļ¬rming the ac-

curacy of (A13-9b). In Table 13-3A, where we let k 0, type 2 dilution is

5.41% (B15 and B16).

Table 13-3B: Summary of Dilution Tradeoffs

In Table 13-3B we summarize the dilution options that we have seen in

Tables 13-2, 13-3, and 13-3A to get a feel for the tradeoffs between type

1 and type 2 dilution. In Table 13-2, where we allowed the ESOP to bear

all dilution, the ESOP experienced dilution of 6.36%. In Table 13-3, by

apportioning one-third of the dilution to him or herself, the seller reduced

type 1 dilution by 6.36% 4.24% 2.12% (Table 13-3B, D8) and under-

took type 2 dilution of 1.80% (D9). The result is that the ESOP bears

dilution of 4.24% (C8) and the owner bears 1.8% (C9). In Table 13-3A we

allowed the seller to bear all dilution rather than the ESOP. The seller

thereby eliminated the 6.36% Type 1 dilution and accepted 5.41% type 2

dilution.

Judging by the results seen in Table 13-3B, it appears that when the

seller takes on a speciļ¬c level of type 2 dilution, the decrease in type 1

dilution is greater than the corresponding increase in type 2 dilution. This

turns out to be correct in all cases, as proven in Appendix A, the Math-

ematical Appendix.

SUMMARY

In this mini-chapter we developed formulas to calculate the post-

transaction values of the ļ¬rm, ESOP, and the payment to the owner, both

pre-transaction and post-transaction, as well as the related dilution. We

also derived formulas for eliminating the dilution as well as for specifying

any desired level of dilution. Additionally, we explored the trade-offs

between type 1 and type 2 dilution.

Advantages of Results

The big advantages of these results are:

1. If the owner insists on being paid at the pre-transaction value,

as most will, the appraiser can now immediately calculate the

dilutive effects on the value of the ESOP and report that in the

initial valuation report.31 Therefore, the employees will be

entering the transaction with both eyes open and will not be

disgruntled and/or suspicious as to why the value, on average,

declines at the next valuation. This will also provide a real

benchmark to assess the impact of the ESOP itself on

proļ¬tability.

31. Many ESOP trustees prefer this information to remain as supplementary information outside of

the report.

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 467

2. For owners who are willing to eliminate the dilution to the

ESOP or at least reduce it, this chapter provides the formulas to

do so and the ability to calculate the trade-offs between type 1

and type 2 dilution.

Function of ESOP Loan

An important byproduct of this analysis is that it answers the question

of what is the function of the ESOP loan. Obviously it functions as a

ļ¬nancing vehicle, but suppose you were advising a very cash rich ļ¬rm

that could fund the payment to the owner in cash. Is there any other

function of the ESOP loan? The answer is yes. The ESOP loan can increase

the value of the ļ¬rm in two ways:

1. It can be used to shield income at the ļ¬rmā™s highest income tax

rate. To the extent that the ESOP payment is large enough to

cause pre-tax income to drop to lower tax brackets, then that

portion shields income at lower than the marginal rate and

lowers the value of the ļ¬rm and the ESOP.

2. If the ESOP payment in the ļ¬rst year is larger than pre-tax

income, the ļ¬rm cannot make immediate use of the entire tax

deduction in the ļ¬rst year. The unused deduction will remain as

a carryover, but it will suffer from a present value effect.

Common Sense Is Required

A certain amount of common sense is required in applying these for-

mulas. In extreme transactions such as those approaching a 100% sale to

the ESOP, we need to realize that not only can tax rates change, but

payments on the ESOP loan may entirely eliminate net income and reduce

the present value of the tax beneļ¬t of the ESOP loan payments. In ad-

dition, the viability of the ļ¬rm itself may be seriously in question, and it

is likely that the appraiser will have to increase the discount rate for a

post-transaction valuation. Therefore, one must use these formulas with

at least two dashes of common sense.

To Whom Should the Dilution Belong?

Appraisers almost unanimously consider the pre-transaction value ap-

propriate, yet there has been considerable controversy on this topic. The

problem is the apparent ļ¬nancial sleight of hand that occurs when the

post-transaction value of the ļ¬rm and the ESOP precipitously declines

immediately after doing the transaction. On the surface, it somehow

seems unfair to the ESOP. In this section we will explore that question.

Analyzing a Simple Sale

Only two aspects relevant to this discussion are unique about a sale to

an ESOP: (1) tax deductibility of the loan principal, and (2) forgiveness

of the ESOPā™s debt. Letā™s analyze a simple sale to a non-ESOP buyer and

later to an ESOP buyer. For simplicity we will ignore tax beneļ¬ts of all

loans throughout this example.

PART 5 Special Topics

468

Suppose the fair market value of all assets is $10 million before and

after the sale. Pre-transaction liabilities are zero, so capital is worth $10

million, pre-transaction. If a buyer pays the seller personally $5 million

for one-half of the capital stock of the Company, the transaction does not

impact the value of the ļ¬rmā”ignoring adjustments for control and mar-

ketability. If the buyer takes out a personal loan for the $5 million and

pays the seller, there is also no impact on the value of the company. In

both cases the buyer owns one-half of a $10 million ļ¬rm, and it was a

fair transaction.

If the corporation takes out the loan on behalf of the buyer but the

buyer ultimately has to repay the corporation, then the real liability is to

the buyer, not the corporation, and there is no impact on the value of the

stockā”it is still worth $5 million. The corporation is a mere conduit for

the loan to the buyer.

What happens to the ļ¬rmā™s value if the corporation takes out and

eventually repays the loan? The assets are still worth $10 million post-

transaction.32 Now there are $5 million in liabilities, so the equity is worth

$5 million. The buyer owns one-half of a ļ¬rm worth $5 million, so his or

her stock is only worth $2.5 million. Was the buyer hoodwinked?

The possible confusion over value clearly arises because it is the cor-

poration itself that is taking out the loan to fund the buyerā™s purchase of

stock, and the corporationā”not the buyerā”ultimately repays the loan.

By having the corporation repay the loan, the other shareholder is for-

giving his or her half of a $5 million loan and thus gifting $2.5 million

to the buyer.33 Thus, the ā˜ā˜buyerā™ā™ ultimately receives a gift of $2.5 million

in the form of company stock. This is true whether the buyer is an in-

dividual or an ESOP.34

Dilution to Nonselling Owners

When there are additional business owners who do not sell to the ESOP,

they experience dilution of their interests without the beneļ¬t of getting

paid. Conceptually, these owners have participated in giving the ESOP a

gift by having the Company repay the debt on behalf of the ESOP.

Assuming the nonselling owner has the fraction q of the outstanding

stock of the ļ¬rm, his or her dilution is equal to:

q[(1 t) pDE e]

dilution to nonselling shareholderā™s stock35 (A13-1g*)

The dilution formula (A13-1g*) tells us that the dilution to the non-

selling shareholder is simply his or her ownership, q, multiplied by the

32. There is a second-order effect of the ļ¬rm being more highly leveraged and thus riskier that

may affect value (and which we are ignoring here). See Chapter 14.

33. The other half of the forgiveness is a washā”the buyer forgiving it to himself or herself.

34. This does not mean that an ESOP brings nothing to the table in a transaction. It does bring tax

deductibility of the loan principal as well as the Section 1042 rollover.

35. One would also need to consider adjusting for each nonselling shareholderā™s control and

marketability attributes. To do so, we would have to add a term in equation (13-1g*)

immediately after the q. The term would be the ownerā™s equivalent of DE, except

customized for his or her ownership attributes. The details of such a calculation are beyond

the scope of this chapter.

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 469

dilution in value to the ļ¬rm itself, which is the sum of the after-tax cost

of the ESOP loan and the lifetime costs.

It is also important to note that equation (A13-1g*) does not account

for any possible increase in value the owner might experience as a result

of having greater relative control of the ļ¬rm. For example, if there were

two 50% owners pre-transaction and one sells 30% to the ESOP, post-

transaction the remaining 50% owner has relatively more control than he

or she had before the transaction. To the extent that we might ascribe

additional value to that increase in relative control, we would adjust the

valuation formulas. This would mitigate the dilution in equation (A13-

1g*).

Legal Issues

As mentioned above, appraisers almost unanimously consider the pre-

transaction value appropriate. Also mentioned earlier in the chapter, case

law and Department of Labor proposed regulations indicate the pre-

transaction value is the one to be used. Nevertheless, there is ongoing

controversy going back to Farnum, a case in which the Department of

Labor withdrew before going to court, that the post-transaction value may

be the most appropriate price to pay the seller.

In the previous section we demonstrated that the ESOP is receiving

a gift, not really paying anything for its stock. Therefore, there is no ec-

onomic justiļ¬cation for reducing the payment to the owner below the

pre-transaction fair market value, which is the price that the seller would

receive from any other buyer. If the ESOP (or any party on its behalf)

demands that it ā˜ā˜payā™ā™ no more than post-transaction value, it is tanta-

mount to saying, ā˜ā˜The gift you are giving me is not big enough.ā™ā™

While the dilution may belong to the ESOP, it is nevertheless an

important consideration in determining the fairness of the transaction for

purposes of a fairness opinion. If a bank loans $10 million to the ESOP

for a 100% sale, with no recourse or personal guarantees of the owner,

we may likely decide it is not a fair transaction to the ESOP and its

participants. We would have serious questions about the ESOPā™s proba-

bility of becoming a long-range retirement program, given the huge debt

load of the Company post-transaction.

Charity

While the dilution technically belongs to the ESOP, I consider it my duty

to inform the seller of the dilution phenomenon and how it works. While

afļ¬rming the sellerā™s right to receive fair market value undiminished by

dilution, I do mention that if the seller has any charitable motivations to

his or her employeesā”which a minority doā”then voluntarily accepting

some of the dilution will leave the Company and the ESOP in better

shape. Of course, in a partial sale it also leaves the remainder of the

ownerā™s stock at a higher value than it would have had with the ESOP

bearing all of the dilution.

PART 5 Special Topics

470

CHAPTER 14

Buyouts of Partners and

Shareholders

INTRODUCTION

AN EXAMPLE OF A BUYOUT

The Solution

First-Order Impact of Buyout on Post-transaction Valuation

Secondary Impact of Buyout on Post-transaction Valuation

ESOP Dilution Formula as a Benchmark

EVALUATING THE BENCHMARKS

471

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INTRODUCTION

Buying out a partner or shareholder is intellectually related to the prob-

lem of measuring dilution in employee stock ownership plans (ESOPs),

which is covered in the previous chapter. There is no substantive differ-

ence in the post-transaction effects of buying out partners versus share-

holders, so for ease of exposition we will use the term partners to cover

both situations.

AN EXAMPLE OF A BUYOUT

Suppose you have already valued the drapery manufacturer owned by

the Roth family, the Drapes of Roth. Its FMV on an illiquid minority

interest basis is $1 million pre-buyout. There are four partners, each with

a 25% share of the business: I. M. Roth, U. R. Roth, Izzy Roth, and B.

Roth. There are 1 million shares issued and outstanding, so the per share

FMV is $1 million FMV/1 million shares $1.00 per share. The problem

is the impact on the post-transaction FMV if the three other Roths become

wroth with Izzy Roth and want to buy him out.

The Solution

The solution to the problem ļ¬rst depends whether the three Roths have

enough money to buy out Izzy with their personal assets. If so, then there

is no impact on the value of the ļ¬rm. If not then the ļ¬rm typically will

take out a loan to buy out Izzy.1

First-Order Impact of Buyout on Post-transaction Valuation

To a ļ¬rst approximation, there should be no impact on the FMV per share.

For simplicity of discussion, we ignore the subtleties of differentials in

the discount for lack of control of 25% versus 33 1/3% interests, although

in actuality the appraiser must consider that issue. The FMV of the ļ¬rm

has declined by the amount of the loan to $750,000. The shareholders

bought 250,000 shares, leaving $750,000 shares. Our ļ¬rst approximation

of the post-transaction value is $750,000/750,000 shares $1.00 per share,

or no change.

Secondary Impact of Buyout on Post-transaction Valuation

The $250,000 has increased the debt-to-equity ratio of the ļ¬rm. The ļ¬rm

has increased its ļ¬nancial risk, which raises the overall risk of the ļ¬rm.2

It is probably appropriate to raise the discount rate 1ā“2% to reļ¬‚ect the

additional risk and rerun the pre-transaction discounted cash ļ¬‚ows to

come to a potential post-transaction valuation. Suppose that value is $0.92

1. It is possible for the shareholders to take out the loan individually and the ļ¬rm would pay it

indirectly by bonusing out sufļ¬ciently large salaries to cover the personally loans above and

beyond their normal draw. This has no impact on the solution, as both the direct and

indirect approaches will come to the same result.

2. In the context of the capital asset pricing model, the stock beta rises with additional ļ¬nancial

leverage.

PART 5 Special Topics

472

per share. Is that reasonable? What if the tentative post-transaction value

were $0.78 per share? Is that reasonable?

ESOP Dilution Formula as a Benchmark

A benchmark would be very helpful to determine reasonability. Letā™s set

up a hypothetical ESOP with tax attributes similar to the partner to be

bought out. A loan to fund this purchase would have no tax advantages.

While the interest is tax deductible, the ļ¬rm does not need to engage in

this buyout transaction in order to achieve its optimal debt to equity ratio

in order to have the minimum possible weighted average cost of capital

(WACC). The ļ¬rm can borrow optimally without a buyout. Therefore, it

is reasonable to consider the after-tax cost of the loan to be the same as

its pre-tax amount, which is the payment to the partner.

The following is a listing and calculation of the various values per-

tinent to this transaction. All values are a fraction of a starting pre-

transaction value of $1.

1 pre-buyout FMV (14-1)

x payment to the partner (14-2)

1 x post-transaction FMVā”Firm (14-3)

The hypothetical ESOP owns p% of the ļ¬rm, where p is the portion

of the partnership bought from the selling partner. Its post-transaction

value is:

p(1 x) post-transaction FMVā”Hypothetical ESOP (14-4)

The ļ¬rst four formulas tell us that for every $1 of pre-transaction value,

the company pays the selling partner x, which leaves a post-transaction

value of the ļ¬rm of 1 x and post-transaction of the ESOPā™s interest in

the partnership of p(1 x).

The company should pay the partner the amount that equates the

payment to the partner with the post-transaction value of the hypothetical

ESOP, or:

x p(1 x) Payment Post-Trans. FMV- Hypothetical ESOP (14-5)

Collecting terms,

x px p (14-5a)

x(1 p) p (14-5b)

Dividing through by 1 p, we come to a ļ¬nal solution of:

p

x (14-6)

1 p

Note that equation (14-6) is identical to equation (13-3j) when e 0,

t 0, and DE 1. This makes sense for the following reasons:

1. This is a buyout of a partner. The ESOP is hypothetical only.

There are no lifetime ESOP costs, which means e 0.

CHAPTER 14 Buyouts of Partners and Shareholders 473

2. There are no tax beneļ¬ts of the loan to buy out the partner.

Therefore, tax savings on the hypothetical ESOP loan are zero

and t 0.

3. There are no ESOP level marketability attributes of marketability

1.3

and control in the buyout of the partner, therefore DE

Substituting p 25% into equation (14-6), x 20%. Letā™s check the re-

sults.

1. The Company pays 20% of the pre-transaction value to the

partner

2. The post-transaction value is the remaining 80%.

3. There are three real partners remaining plus the hypothetical

ESOP, for a total of four partners

4. Each remaining partner has a 1ā„4 share of the 80%, or 20%,

which is equal to the payment to the ļ¬rst partner. This

demonstrates that equation (14-6) works.

Thus, for every $1.00 of pre-transaction value, this hypothetical ESOP

benchmark leaves us with $0.80 per share post-transaction value.

EVALUATING THE BENCHMARKS

If the transaction would not increase ļ¬nancial risk, the post-transaction

value of the ļ¬rm would be the same as the pre-transaction value, or $1.00

per share. Incorporating the leverage into the valuation, we have results

of $0.92 per share and $0.78 per share using two different additions to

the discount rate in our discounted cash ļ¬‚ow analysis. Our hypothetical

ESOP benchmark value is $0.80 per share. What is reasonable?

It is clear that the post-transaction value cannot be more than the

pre-transaction value, so the latter is a ceiling value. It is also clear that

the hypothetical ESOP approach is a ļ¬‚oor value, because the ESOP really

does not exist and the 250,000 shares are really not outstanding. The hy-

pothetical ESOP approach assumes the shares are outstanding. Therefore,

the post-transaction value must be higher than the hypothetical ESOP

value.

Now we know the post-transaction value of the ļ¬rm should be less

than $1.00 per share and greater than $0.80 per share. The $0.92 per share

post-transaction value looks quite reasonable, while the $.78 per share

value is obviously wrong. If we had added 1% to the discount rate to

arrive at the $0.92 per share and 2% to the discount rate to produce the

$0.78 per share result, the 1% addition would appear to be the right one.

3. However, this is where the differences mentioned earlier, i.e., differences in the discount for lack

of control of a 25% partner versus a 1/3 partner, would come into play.

PART 5 Special Topics

474

Glossary

ADF (annuity discount factor) the present value of a ļ¬nite stream of

cash ļ¬‚ows for every beginning $1 of cash ļ¬‚ow. See Chapter 3.

control premium the additional value inherent in the control interest as

contrasted to a minority interest, which reļ¬‚ects its power of control1

CARs (cumulative abnormal returns) a measure used in academic ļ¬-

nance articles to measure the excess returns an investor would have re-

ceived over a particular time period if he or she were invested in a par-

ticular stock. This is typically used in control and takeover studies, where

stockholders are paid a premium for being taken over. Starting some time

period before the takeover (often ļ¬ve days before the ļ¬rst announced bid,

but sometimes a longer period), the researchers calculate the actual daily

stock returns for the target ļ¬rm and subtract out the expected market

returns (usually calculated using the ļ¬rmā™s beta and applying it to overall

market movements during the time period under observation). The excess

actual return over the capital asset pricing model-determined expected

return market is called an ā˜ā˜abnormal return.ā™ā™ The cumulation of the daily

abnormal returns over the time period under observation is the CAR. The

term CAR( 5, 0) means the CAR calculated from ļ¬ve days before the

announcement to the day of announcement. The CAR( 1, 0) is a control

premium, although Mergerstat generally uses the stock price ļ¬ve days

before announcement rather than one day before announcement as the

denominator in its control premium calculation. However, the CAR for

any period other than ( 1, 0) is not mathematically equivalent to a con-

trol premium.

DLOC (discount for lack of control) an amount or percentage deducted

from a pro rata share of the value of 100% of an equity interest in a

business, to reļ¬‚ect the absence of some or all of the powers of control.2

DLOM (discount for lack of marketability) an amount or percentage

deducted from an equity interest to reļ¬‚ect lack of marketability.3

1. Business Valuation Standards, Deļ¬nitions, American Society of Appraisers.

2. Ibid.

3. Ibid.

475

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economic components model Abramsā™ model for calculating DLOM

based on the interaction of discounts from four economic components.

This model consists of four components: the measure of the economic

impact of the delay-to-sale, monopsony power to buyers, and incremental

transactions costs to both buyers and sellers. See the second half of Chap-

ter 7.

discount rate the rate of return on investment that would be required

by a prudent investor to invest in an asset with a speciļ¬c level risk. Also,

a rate of return used to convert a monetary sum, payable or receivable

in the future, into present value.4

fractional interest discount the combined discounts for lack of control

and marketability.

g the constant growth rate in cash ļ¬‚ows or net income used in the ADF,

Gordon model, or present value factor.

Gordon model present value of a perpetuity with growth. The end-of-

year Gordon model formula is 1/(r g), and the midyear formula is

1 r/(r g). See Chapter 3.

log size model Abramsā™ model to calculate discount rates as a function

of the logarithm of the value of the ļ¬rm. See Chapter 4.

markup the period after an announcement of a takeover bid in which

stock prices typically rise until a merger or acquisition is made (or until

it falls through).

Ordinary least squares (OLS) regression analysis a statistical technique

that minimizes the sum of the squared deviations between a dependent

variable and one or more independent variables and provides the user

with a y-intercept and x-coefļ¬cients, as well as feedback such as R2 (ex-

plained variation/total variation) t-statistics, p-values, etc. See Chapter 2.

NPV (net present value of cash ļ¬‚ows) Same as PV, but usually includes

a subtraction for an initial cash outlay.

PPF (periodic perpetuity factor) a generalization formula invented by

Abrams that is the present value of regular but noncontiguous cash ļ¬‚ows

that have constant growth to perpetuity. The end-of-year PPF is equal to:

r)b

(1

PPF

r) j g) j

(1 (1

and the midyear PPF is equal to

r)b

1 r (1

PPF

r) j g) j

(1 (1

where r is the discount rate, b is the number of years (before) since the

last occurrence of the cash ļ¬‚ow, and j is the number of years between

cash ļ¬‚ows. See Chapter 3.

PV (present value of cash ļ¬‚ows) the value in todayā™s dollars of cash

ļ¬‚ows that occur in different time periods.

4. Ibid.

Glossary

476

r)n, where n is the

present value factor equal to the formula 1/(1

number of years from the valuation date to the cash ļ¬‚ow and r is the

discount rate. For business valuation, n should usually be midyear, i.e.,

n 0.5, 1.5, . . .

QMDM (quantitative marketability discount model) model for calcu-

lating DLOM for minority interests.5

r the discount rate

runup the period before a formal announcement of a takeover bid in

which one or more bidders are either preparing to make an announce-

ment or speculating that someone else will.

5. Z. Christopher, Mercer, Quantifying Marketability Discounts: Developing and Supporting Marketability

Discounts in the Appraisal of Closely Held Business Interests (Memphis, Tenn: Peabody, 1997)

Glossary 477

Index

Amihud, Y., 232, 282, 379, 381 Freeman, Neill, 233ā“234, 283

Andersson, Thomas, 219, 283 French, Kenneth R., 119, 146, 155

Annin, Michael, 148, 155

Gilbert, Gregory A., 146, 155, 167

Glass, Carla, 208, 224, 226

Banz, Rolf, 119, 155

Golder, Stanley C., 410, 431

Barca, F., 220, 282

Gordon, M.J., 59, 90n

Bergstrom, C., 282

Gordon model, 25, 50, 59ā“60, 63ā“79, 87ā“90, 93ā“

Berkovitch, E., 221, 282

97, 140, 153, 157, 175ā“176, 207, 230, 263ā“264,

Bhattacharyya, Gouri K., 22, 52

287, 385ā“387, 392, 394, 396, 398ā“399, 403

Black, Fisher, 303

Grabowski, Roger, 113, 119, 126, 144, 146, 148ā“

Black-Scholes options pricing model (BSOPM),

151, 155, 166, 241

192, 235, 246, 251ā“254, 256, 281, 303, 305ā“306

Gregory, Gordon, 258n

Black-Scholes put option, 233, 243ā“246, 298, 306

Guideline Company Method, 46ā“52, 59, 114,

Boatwright, David, 258n

153, 167ā“168

Bolotsky, Michael J., 198, 200ā“206, 230ā“231, 282

Bradley, M.A., 210, 220, 224ā“225, 233, 282

Brealey, R.A., 175, 177

Hall, Lance, 236, 298

Hamada, R.S., 183, 190

Harris, Ellie G., 222, 282

Center for Research in Security Prices (CRSP),

Harrison, Paul, 113, 131, 133ā“135, 155

162n

Hayes, Richard, 134, 155

Chaffe, David B.H., 241ā“242, 251, 282, 307, 317

Hiatt, R.K., 246n, 262n, 287n, 405n

Copeland, Tom, 176

Hogarth, Robin M., 250, 282

Crow, Matthew R., 249

Horner, M.R., 220, 282

Houlihan Lokey Howard & Zukin (HLHZ)

studies, 198, 206, 210, 212ā“213, 217, 226, 329n

Desai, A., 210, 220, 224ā“225, 233, 282 Hull, John C., 241n

Eckbo, B.E., 220ā“221, 282 Ibbotson & Associates, 120, 134, 147n, 148, 155,

Einhorn, Hillel J., 250, 282 162, 170, 176ā“177, 385, 387, 404

Ellsberg, Daniel, 250, 282 Ibbotson, Roger G., 139n, 147, 151, 154ā“155, 207

Eulerā™s constant, 49, 51 Indro Daniel C., 175, 177

Excel, 2, 44, 51, 115, 124, 136 Institute of Business Appraisers (IBA), 272ā“273

Fagan, Timothy J., 214, 217, 283 Jacobs, Bruce I., 119, 152ā“153, 155, 167

Fama, Eugene F., 119, 146, 155 Jankowske, Wayne C., 200ā“201, 204ā“206, 231,

Fama-French Cost of Equity Model, 147ā“148 282

Fowler, Bradley, 405, 410ā“411, 414ā“415, 431 Johnson, Bruce A., 274, 276, 282

Franks, J.R., 221, 282 Johnson, Richard A., 22, 52

479

Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.

Joyce, Allyn A., 170, 177 Neal, L., 134, 155

Julius, J. Michael, 249 Newton, Isaac, 156

Obenshain, Douglas, 258n

Kahneman, Daniel, 247, 284

Kaplan, Paul D., 147, 155

Kasper, Larry J., 88n, 222, 234ā“235, 281ā“282

Pacelle, Mitchell, 411, 431

Kasper bid-ask spread model, 191, 222, 234ā“235

Paudyal, Krishna, 210, 222, 235, 283

Kasper discounted time to market model, 232

Peterson, James D., 147, 155

Kim, E.H., 210, 220, 224ā“225, 233, 282

Phillips, John R., 233ā“234, 283

King, David, 113, 119, 126, 144, 146, 148ā“151,

Plummer, James L., 410, 431

155, 166, 241, 282

Polacek, Tim, 236, 298

Koller, Tim, 176

Pratt, Shannon P., 18, 19, 42, 46, 52, 207, 235,

253, 283, 350, 364, 381

Pratt, Stanley E., 431

Lang, L.H.P., 221, 282

Lease, Ronald C., 210, 212, 214, 217, 219, 227,

231, 280 Reilly, Robert F., 18, 19, 42, 46, 52, 235, 251, 253,

Lee, Wayne Y., 175, 177 283

Lerch, Mary Ann, 282 Roach, George P., 206, 221, 224ā“225, 283

Levy, H., 220, 283 Roll, Richard, 210, 283

Levy, Kenneth N., 119, 152ā“153, 155, 167 Rothschild, Baron, 134n

Lotus, 2, 44ā“45, 124, 136 Rydqvist, K., 220, 279, 282ā“283

Schilt, James H., 281

Maher, Maria, 219, 283

Schweihs, Robert P., 18, 19, 42, 46, 52, 235, 251,

Management Planning, Inc., 235ā“241, 250ā“251,

253, 283

255ā“256, 273ā“275, 279, 298ā“303, 330

Schwert, G. William, 151ā“152, 155, 192, 209ā“211,

Maquieira, Carlos P., 210, 220ā“221, 224ā“227,

220ā“222, 235, 255, 269, 283, 335n

283

Scholes, Myron, 303

McCarter, Mary M., 208, 224, 226, 282

Scott, William Jr., 140n

McConnell, John J., 210, 212, 213ā“214, 217, 219,

Seguin, Paul J., 151ā“152, 155

227, 231, 282ā“283

Shannon, Donald, 3

Megginson, William L., 210, 212ā“214, 219ā“221,

Shapiro, E., 59, 90n

224ā“227, 283

Sharpe-Lintner model, 146

Mendelson, Haim, 232, 282, 379, 381

Simpson, David W., 283

Menyah, Kojo, 210, 222, 235, 281

Solomon, King, 134

Mercer, Z. Christopher, 59, 90n, 191ā“192, 197,

Stern, Joel, 281

200ā“203, 206ā“209, 224ā“226, 232ā“235, 248ā“249,

Stillman, R., 220, 283

252, 273ā“281, 283, 317, 350, 477n

Stoll, H.R., 223, 283

Mercer Quantitative Marketability Discount

Stulz, R., 282

Model (QMDM), 2, 59, 89, 191, 232ā“234, 248ā“

249, 273ā“281, 477

Mergerstat Review, 198, 201, 203, 209n, 225,

Thomas, George B. Jr., 155ā“156

233ā“234

Tversky, Amos, 247, 284

Meyers, Roy H., 235n

Twain, Mark, 170

Mikkelson, Wayne H., 210, 212ā“214, 217, 219,

227, 231, 282

Miles, Raymond, 272, 359n, 379, 381

Vander Linden, Eric, 207, 284

Miller, Merton, 449n

Modigliani, Franco, 449n

Morris, Jane K., 431 Walkling, R.A., 280

Much, Paul J., 214, 283 Watson, John Jr., 236n, 255n

Murrin, Jack, 176 Williams, J.B., 59n, 90n

Myers, Stewart C., 175ā“177, 411 Wonnacott, Thomas H., 22, 52

Wonnacott, Ronald J., 22, 52

Nail, Lance, 210, 220ā“221, 224ā“227, 283

Nath, Eric 200ā“204, 206ā“209, 227, 283 Zingales, L., 220, 284

Narayanan, M. P., 221, 282 Zukin, James H., 207, 284

Index

480

About the Author

Jay B. Abrams, ASA, CPA, MBA, a nationally known authority in valuing

privately held businesses, has published numerous seminal articles.

Mr. Abrams is the principal of Abrams Valuation Group in La Jolla,

California, a ļ¬rm that specializes in business valuation. He was a Project

Manager at Arthur D. Little Valuation, Inc. in Los Angeles, California,

where he performed the valuations of Columbia Pictures, Dr. Pepper,

Purex, MCO Geothermal, VSA, and many other large ļ¬rms.

Mr. Abrams has several inventions to his name, many of which are

discussed in this work. In 1992 he published the solution to a 500-year-

old problemā”how to pinpoint an accounting transposition error.

Mr. Abrams has an MBA in ļ¬nance from the University of Chicago,

where he also took graduate courses in the Department of Economics. He

received his B.S. in Business Administration from California State Uni-

versity, Northridge, where he received the Arthur Young Outstanding

Accounting Student Award in 1972.

Mr. Abrams has spoken in a variety of different professional and

public forums about valuing privately held businesses, including the 1998

Conference of the National Association of Valuation Analysts; the 1996

International Conference of the American Society of Appraisers, in To-

ronto; Anthony Robbinsā™ Mastery University; and the National Center for

Employee Ownership Annual Conference. He has taught business valu-

ation as continuing legal education and at the University of California at

San Diego Extension.

Mr. Abrams lives in San Diego, California, with his wife and ļ¬ve

children.

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