433

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Advantages of Results

Function of ESOP Loan

Common Sense Is Required

To Whom Should the Dilution Belong?

De¬nitions

The Mathematics of the Post-transaction Fair Market Value Balance

Sheet

Analyzing a Simple Sale

Dilution to Non-selling Owners

Legal issues

Charity

APPENDIX A: MATHEMATICAL APPENDIX

APPENDIX B: SHORTER VERSION OF CHAPTER 13

PART 5 Special Topics

434

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.

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

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.

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.

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.

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.

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

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%

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

PART 5 Special Topics

436

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

iteration

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

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).

T A B L E 13-1

Calculation of Lifetime ESOP Costs

A B

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

438

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.

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)