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103, American Society of Appraisers, Herndon, Virginia.


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Advantages of Results
Function of ESOP Loan
Common Sense Is Required
To Whom Should the Dilution Belong?
The Mathematics of the Post-transaction Fair Market Value Balance
Analyzing a Simple Sale
Dilution to Non-selling Owners
Legal issues

PART 5 Special Topics
This chapter is the result of further thought and research on my treatment
of valuing ESOPs (Abrams 1993 and 1997). It not only simpli¬es those
articles, but it goes far beyond them. Reading them is not necessary for
understanding this chapter.

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
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-
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.

What Can Be Skipped
This chapter contains much tedious algebra. For readers who wish to skip
all of the mathematics and optional sections and simply get the bottom
line can read the ˜˜quick-and-dirty™™ version of this chapter in Appendix
B. The section on the iterative approach can be safely skipped, as it en-
hances the understanding of dilution but contains no additional formulas
of practical signi¬cance.

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.

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 435
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 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-
partment of Labor proposed regulations indicate that the pre-transaction
value should be used.2

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
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.
p percentage of ¬rm sold to the ESOP, assumed at 30%
t combined federal and state corporate income tax rate, assumed
at 40%

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

PART 5 Special Topics
r the annual loan interest rate, assumed at 10%
i the monthly loan interest rate r/12 0.8333% monthly
V1B the pre-transaction value of 100% of the stock of the ¬rm
after discounts and premiums at the ¬rm level but before those at
the ESOP level,3 assumed at $1,000,000, as shown in Table 13-2.
The B subscript means before considering the lifetime cost of
initiating and maintaining the ESOP (see E, e, and VjA below). V1B
does not consider the cost of the loan. This differs from VjB, as
described below.
V1A Same as V1B, except this is the pre-transaction value after
deducting the lifetime cost of initiating and maintaining the ESOP
(see E, e, and VjA below) but before considering the loan. Note this
differs from VjA, where j 1, where we do subtract the cost of the
ESOP loan as of iteration j 1.
VjB the value of the ¬rm at the jth iteration before deducting the
lifetime ESOP costs (see E below) but after subtracting the net
present value of the ESOP loan (see NPLV) as calculated in
iteration j 1 (for j 1).
VjA the value of the ¬rm at the jth iteration after deducting the
lifetime ESOP costs (see immediately below) and the ESOP loan as
of the ( j 1)st iteration.
Vn the ¬nal post-transaction value of the ¬rm, i.e., at the nth
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 $40,000.4
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
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%.5 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

3. In Abrams (1993) the discounts and premiums at the ¬rm level are a separate variable. This
treatment is equally as accurate and is simpler.
4. How to calculate the pre-transaction value of the ¬rm is outside the scope of this article.
5. These are arbitrary assumptions chosen for mathematical ease.

CHAPTER 13 ESOPs: Measuring and Apportioning Dilution 437
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.
Lj the amount of the ESOP Loan in iteration j, which equals the
payment to the owner. That equals the FMV of the ¬rm in
iteration j multiplied by pDE, the percentage of the ¬rm being sold
to the ESOP, multiplied again by the factor for discounts or
premiums at the ESOP level. Mathematically, Lj pDE VjA. Note:
this de¬nition only applies in the Iterative Approach where we are
eliminating type 1 dilution.
NPVLj the after-tax, net present value of the ESOP loan as
calculated in iteration j. The formula is NPVLj (1 t)Lj, as
explained below.
n The number of iterations
D1 type 1 dilution (dilution to the ESOP)
D2 type 2 dilution (dilution to the seller)
FMV fair market value

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).

T A B L E 13-1

Calculation of Lifetime ESOP Costs


5 Pre-tax annual ESOP costs $10,000
6 After-tax annual ESOP costs (1 t) * pre-tax 6,000
7 Required rate of return r 25%
8 Perpetual growth of ESOP costs g 5%
9 Gordon model multiple (end year) 1/(r g) 5.000
10 Capitalized annual costs 30,000
11 Initial outlay-pre-tax 20,000
12 Initial outlay-after-tax (1 t) * pre-tax 12,000
13 Lifetime ESOP costs 42,000
14 Lifetime ESOP costs-rounded to (used in Table 13-2, B9) $40,000

PART 5 Special Topics
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.6 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.

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)


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