<< . .

. 63
( : 66)

. . >>

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.20 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.21

Dilution to Non-Selling 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.
To calculate the dilution to other owners, we begin with the post-
transaction value of the ¬rm in equation (13-1e) and repeat the equation
as (13-1e*). Then we will calculate the equivalent equations for the non-
selling owner as we did for the ESOP in equations (13-1f) and (13-1g),
and we will relabel those equations by adding an asterisk.
1 (1 t)pDE e
post-transaction value of the firm (repeated) (13-1e*)
If the nonselling shareholder owns the fraction q of the outstanding stock,
then his or her post-transaction value is:

19. 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.
20. The other half of the forgiveness is a wash”the buyer forgiving it to himself or herself.
21. 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.

PART 5 Special Topics
q q(1 t)pDE qe
post-transaction value of nonselling shareholder™s stock (13-1f*)
Finally, we calculate dilution to the nonselling shareholder as his or her
pre-transaction value of q minus the pre-transaction value in equation
(13-1f*), or:
q[(1 t)pDE e]
dilution to nonselling shareholder™s stock22 (13-1g*)
The dilution formula (13-1g*) tells us that the dilution to the non-
selling shareholder is simply his or her ownership, q, multiplied by the
dilution in value to the ¬rm itself, which is the sum of the after-tax cost
of the ESOP loan and the lifetime costs. Here, because we are not mul-
tiplying by the ESOP™s ownership modi¬ed for its unique marketability
and control attributes, we do not get the squared terms that we did in
equation (13-1f) and (13-1g).
It is also important to note that equations (13-1f*) and (13-1g*) do
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 con-
trol 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 equa-
tion (13-1g*).

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
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

22. 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 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.

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.

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.

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.
1 (1 t)pDE 1 (A13-3)
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
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.
1 (A13-5)
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.

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.

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-
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.

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 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
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
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%
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

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
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

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)
t)p 2D2
pDE [pDE (1 pDE e]

t)p 2D2
(1 pDE e dilution to ESOP (A13-7g)

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

<< . .

. 63
( : 66)

. . >>