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

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INTRODUCTION

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

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

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

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

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

both situations.

AN EXAMPLE OF A BUYOUT

Suppose you have already valued the drapery manufacturer owned by

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

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

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

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

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

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

wroth with Izzy Roth and want to buy him out.

The Solution

The solution to the problem ¬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

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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

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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