<<

. 18
( 18)



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 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 ESOP™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
af¬rming the seller™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 employees”which a minority do”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
owner™s stock at a higher value than it would have had with the ESOP
bearing all of the dilution.


BIBLIOGRAPHY
Abrams, Jay B. 1993. ˜˜An Iterative Procedure to Value Leveraged ESOPs.™™ Valuation (Jan-
uary): 71“103.
” ”. 1997. ˜˜ESOPs: Measuring and Apportioning Dilution.™™ Valuation (June): 3“25.

Miller, Merton, and Franco Modigliani. 1958. ˜˜The Cost of Capital, Corporation Finance,
and the Theory of Investment.™™ American Economic Review 48: 61“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 de¬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


Signi¬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 ¬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
signi¬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 ¬rm and the ESOP.
There are several types of problems relating to the dilution phenom-
enon:
1. The technical problem of de¬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
win“win instead of win“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 win“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 de¬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 de¬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 ¬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 de¬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 de¬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 ¬rm™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 speci¬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 ¬rm, but that is beyond the scope of this book.


De¬ning Terms
We ¬rst de¬ne some of terms appearing in the various equations.
Let:
p percentage of ¬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 ¬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 ¬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 ESOP™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 ¬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). Let™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 ¬rst year™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 de¬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 ¬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 Equations”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 ¬rm:
1 (1 t)pDE e post-transaction value of the firm (A13-7e)
Since the ESOP owns p% of the ¬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 ESOP™s p% of the ¬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 ¬rm when all dilution goes to the ESOP, let™s look at a concrete ex-
ample in Table 13-2. The table consists of three sections. Section 1, rows
5“10, is the operating parameters of the model. Section 2 shows the cal-
culation of the post-transaction values of the ¬rm, ESOP, and the dilution
to the ESOP according to equations (A13-7e), (A13-7f), and (A13-7g), re-
spectively, in rows 12“18. Rows 21“26 prove the accuracy of the results,
as explained below.
Section 3 shows the calculation of the post-transaction values of the
¬rm and the ESOP when there is no dilution to the ESOP. We will cover
that part of the table later. In the meantime, let™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 ¬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 ¬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 21“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 ¬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 FMV”¬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 ¬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 ¬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 ¬rm is:
1 e
post-transaction value of the firm”
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 Calculations”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 ¬rm pays.
2. The ¬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 ¬nal value of the ¬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 ¬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 seller”as in equation (A13-
9a)”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, con¬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 speci¬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 ¬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
pro¬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
¬nancing vehicle, but suppose you were advising a very cash rich ¬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 ¬rm in two ways:
1. It can be used to shield income at the ¬rm™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 ¬rm and the ESOP.
2. If the ESOP payment in the ¬rst year is larger than pre-tax
income, the ¬rm cannot make immediate use of the entire tax
deduction in the ¬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 bene¬t of the ESOP loan payments. In ad-
dition, the viability of the ¬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 ¬nancial sleight of hand that occurs when the
post-transaction value of the ¬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 ESOP™s debt. Let™s analyze a simple sale to a non-ESOP buyer and
later to an ESOP buyer. For simplicity we will ignore tax bene¬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 ¬rm”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 ¬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
stock”it is still worth $5 million. The corporation is a mere conduit for
the loan to the buyer.
What happens to the ¬rm™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 ¬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 buyer™s purchase of
stock, and the corporation”not the buyer”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 ˜˜buyer™™ 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 bene¬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 ¬rm, his or her dilution is equal to:
q[(1 t) pDE e]
dilution to nonselling shareholder™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 ¬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 wash”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 shareholder™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 owner™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 ¬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 ¬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 justi¬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 ˜˜pay™™ no more than post-transaction value, it is tanta-
mount to saying, ˜˜The gift you are giving me is not big enough.™™
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 ESOP™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
af¬rming the seller™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 employees”which a minority do”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
owner™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




Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
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 ¬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 ¬rm. If not then the ¬rm typically will
take out a loan to buy out Izzy.1

First-Order Impact of Buyout on Post-transaction Valuation
To a ¬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 ¬rm
has declined by the amount of the loan to $750,000. The shareholders
bought 250,000 shares, leaving $750,000 shares. Our ¬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 ¬rm. The ¬rm
has increased its ¬nancial risk, which raises the overall risk of the ¬rm.2
It is probably appropriate to raise the discount rate 1“2% to re¬‚ect the
additional risk and rerun the pre-transaction discounted cash ¬‚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 ¬rm would pay it
indirectly by bonusing out suf¬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 ¬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. Let™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 ¬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 ¬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 FMV”Firm (14-3)
The hypothetical ESOP owns p% of the ¬rm, where p is the portion
of the partnership bought from the selling partner. Its post-transaction
value is:
p(1 x) post-transaction FMV”Hypothetical ESOP (14-4)
The ¬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 ¬rm of 1 x and post-transaction of the ESOP™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 ¬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 bene¬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%. Let™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 1„4 share of the 80%, or 20%,
which is equal to the payment to the ¬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 ¬nancial risk, the post-transaction
value of the ¬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 ¬‚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 ¬‚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 ¬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 ¬nite stream of
cash ¬‚ows for every beginning $1 of cash ¬‚ow. See Chapter 3.
control premium the additional value inherent in the control interest as
contrasted to a minority interest, which re¬‚ects its power of control1
CARs (cumulative abnormal returns) a measure used in academic ¬-
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 ¬ve days before the ¬rst announced bid,
but sometimes a longer period), the researchers calculate the actual daily
stock returns for the target ¬rm and subtract out the expected market
returns (usually calculated using the ¬rm™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 ˜˜abnormal return.™™ 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 ¬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 ¬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 re¬‚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 re¬‚ect lack of marketability.3


1. Business Valuation Standards, De¬nitions, American Society of Appraisers.
2. Ibid.
3. Ibid.




475




Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
economic components model Abrams™ 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 speci¬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 ¬‚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 Abrams™ model to calculate discount rates as a function
of the logarithm of the value of the ¬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-coef¬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 ¬‚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 ¬‚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 ¬‚ow, and j is the number of years between
cash ¬‚ows. See Chapter 3.
PV (present value of cash ¬‚ows) the value in today™s dollars of cash
¬‚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 ¬‚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, 233“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, 59“60, 63“79, 87“90, 93“
Berkovitch, E., 221, 282
97, 140, 153, 157, 175“176, 207, 230, 263“264,
Bhattacharyya, Gouri K., 22, 52
287, 385“387, 392, 394, 396, 398“399, 403
Black, Fisher, 303
Grabowski, Roger, 113, 119, 126, 144, 146, 148“
Black-Scholes options pricing model (BSOPM),
151, 155, 166, 241
192, 235, 246, 251“254, 256, 281, 303, 305“306
Gregory, Gordon, 258n
Black-Scholes put option, 233, 243“246, 298, 306
Guideline Company Method, 46“52, 59, 114,
Boatwright, David, 258n
153, 167“168
Bolotsky, Michael J., 198, 200“206, 230“231, 282
Bradley, M.A., 210, 220, 224“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, 133“135, 155
162n
Hayes, Richard, 134, 155
Chaffe, David B.H., 241“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, 212“213, 217, 226, 329n
Desai, A., 210, 220, 224“225, 233, 282 Hull, John C., 241n


Eckbo, B.E., 220“221, 282 Ibbotson & Associates, 120, 134, 147n, 148, 155,
Einhorn, Hillel J., 250, 282 162, 170, 176“177, 385, 387, 404
Ellsberg, Daniel, 250, 282 Ibbotson, Roger G., 139n, 147, 151, 154“155, 207
Euler™s constant, 49, 51 Indro Daniel C., 175, 177
Excel, 2, 44, 51, 115, 124, 136 Institute of Business Appraisers (IBA), 272“273


Fagan, Timothy J., 214, 217, 283 Jacobs, Bruce I., 119, 152“153, 155, 167
Fama, Eugene F., 119, 146, 155 Jankowske, Wayne C., 200“201, 204“206, 231,
Fama-French Cost of Equity Model, 147“148 282
Fowler, Bradley, 405, 410“411, 414“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, 234“235, 281“282
Pacelle, Mitchell, 411, 431
Kasper bid-ask spread model, 191, 222, 234“235
Paudyal, Krishna, 210, 222, 235, 283
Kasper discounted time to market model, 232
Peterson, James D., 147, 155
Kim, E.H., 210, 220, 224“225, 233, 282
Phillips, John R., 233“234, 283
King, David, 113, 119, 126, 144, 146, 148“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, 224“225, 283
Levy, H., 220, 283 Roll, Richard, 210, 283
Levy, Kenneth N., 119, 152“153, 155, 167 Rothschild, Baron, 134n
Lotus, 2, 44“45, 124, 136 Rydqvist, K., 220, 279, 282“283


Schilt, James H., 281
Maher, Maria, 219, 283
Schweihs, Robert P., 18, 19, 42, 46, 52, 235, 251,
Management Planning, Inc., 235“241, 250“251,
253, 283
255“256, 273“275, 279, 298“303, 330
Schwert, G. William, 151“152, 155, 192, 209“211,
Maquieira, Carlos P., 210, 220“221, 224“227,
220“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, 213“214, 217, 219,
Seguin, Paul J., 151“152, 155
227, 231, 282“283
Shannon, Donald, 3
Megginson, William L., 210, 212“214, 219“221,
Shapiro, E., 59, 90n
224“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, 191“192, 197,
Stern, Joel, 281
200“203, 206“209, 224“226, 232“235, 248“249,
Stillman, R., 220, 283
252, 273“281, 283, 317, 350, 477n
Stoll, H.R., 223, 283
Mercer Quantitative Marketability Discount
Stulz, R., 282
Model (QMDM), 2, 59, 89, 191, 232“234, 248“
249, 273“281, 477
Mergerstat Review, 198, 201, 203, 209n, 225,
Thomas, George B. Jr., 155“156
233“234
Tversky, Amos, 247, 284
Meyers, Roy H., 235n
Twain, Mark, 170
Mikkelson, Wayne H., 210, 212“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., 175“177, 411 Wonnacott, Thomas H., 22, 52
Wonnacott, Ronald J., 22, 52

Nail, Lance, 210, 220“221, 224“227, 283
Nath, Eric 200“204, 206“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 ¬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 ¬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 problem”how to pinpoint an accounting transposition error.
Mr. Abrams has an MBA in ¬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 Robbins™ 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 ¬ve
children.




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