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