Quantitative business valuation jay b abrams 2nd edition

Quantitative Business Valuation Quantitative Business Valuation A Mathematical Approach for Today’s Professionals Second Edition JAY B ABRAMS John Wiley & Sons, Inc Copyright C 2010 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the Web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at www.wiley.com/go/permissions Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books For more information about Wiley products, visit our Web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Abrams, Jay B Quantitative business valuation : a mathematical approach for today’s professionals / Jay B Abrams — 2nd ed p cm Includes index ISBN 978-0-470-39016-0 (cloth) Business enterprises—Valuation—Mathematical models I Title HF5681.V3A28 2010 657 73—dc22 2009042697 Printed in the United States of America 10 To my father, Leonard Abrams, who taught me how to write To my mother, Marilyn Abrams, who taught me mathematics To my wife, Cindy, who believes in me To my children, Yonatan, Binyamin, Miriam, Nechamah Leah, and Rivkah, who gave up countless Sundays with Abba (Dad) for this book To my great teachers, Mr Ohshima and Christopher Hunt, who brought me to my power to make this happen And finally, to R K Hiatt and Scott Deifik, who caught my mistakes and made significant contributions to the thought that permeates this book Contents List of Tables and Figures xiii Introduction xxi Acknowledgments xxvii PART I FORECASTING CASH FLOW CHAPTER Cash Flow: A Mathematical Derivation CHAPTER CHAPTER Introduction The Mathematical Model Analysis of the Mathematical Model Summary References 11 25 27 27 Forecasting Cash Flow: Mathematics of the Payout Ratio 29 Introduction The Mathematics Forecasting Gross Cash Flow Is Incorrect Conclusion References 31 32 43 44 44 Using Regression Analysis 45 Introduction Forecasting Costs and Expenses Performing Regression Analysis Use of Regression Statistics to Test the Robustness of the Relationship Problems with Regression Analysis for Forecasting Costs Using Regression Analysis to Forecast Sales Autocorrelation in Time Series Analysis 47 48 51 52 63 64 69 vii viii Contents Application of Regression Analysis to the Guideline Company (GC) Methods Summary References 69 73 74 APPENDIX 3A The ANOVA Table (Table A3.1, Rows 28–32) 75 CHAPTER Annuity Discount Factors and the Gordon Model 79 Introduction ADF with End-of-Year Cash Flows Midyear Cash Flows Starting Periods Other Than Year Periodic Perpetuity Factors (PPFs): Perpetuities for Periodic Cash Flows ADFs in Loan Mathematics Relationship of the Gordon Model to the Price/Earnings and Price/Sales Ratios The Bias in Annual (versus Monthly) Discounting Is Immaterial Conclusions References 81 83 91 93 101 107 110 113 119 121 APPENDIX 4A Mathematical Appendix 123 APPENDIX 4B Mathematical Appendix: Monthly ADFs 141 PART II CALCULATING DISCOUNT RATES 145 CHAPTER Discount Rates as a Function of Log Size 149 Research Included in the First Edition Table 5.1: Analysis of Historical Stock Returns Application of the Log Size Model Discussion of Models and Size Effects Industry Effects The Wedge between Public and Private Firm Valuations Satisfying Revenue Ruling 59-60 Summary and Conclusions References 151 152 167 181 191 Automating Iteration Using Newton’s Method 203 APPENDIX 5A 192 196 198 199 ix Contents APPENDIX 5B Mathematical Appendix 207 APPENDIX 5C Abbreviated Review and Use 211 CHAPTER Arithmetic versus Geometric Means: Empirical Evidence and Theoretical Issues 223 Introduction Theoretical Superiority of the Arithmetic Mean Empirical Evidence of the Superiority of the Arithmetic Mean Indro and Lee Article References 225 226 An Iterative Valuation Approach 235 Introduction Equity Valuation Method Invested Capital Approach Log Size Summary References 237 237 243 245 245 247 PART III ADJUSTING FOR CONTROL AND MARKETABILITY 249 CHAPTER Adjusting for Levels of Control and Marketability 253 Introduction The Value of Control and Adjusting for Level of Control Discount for Lack of Marketability (DLOM) Conclusion References 257 APPENDIX 8A Mathematical Appendix 365 PART IV PUTTING IT ALL TOGETHER 375 CHAPTER Empirical Testing of Abrams’s Valuation Theory 377 Introduction Table 9.1: Log Size for 1938–1986 Table 9.2: Reconciliation to the IBA Database Calculation of DLOM 379 380 382 387 CHAPTER 227 232 233 257 301 358 359 622 About the Author American Society of Appraisers, in Toronto; Anthony Robbins’s Mastery University; and National Center for Employee Ownership Annual Conference He has taught business valuation as continuing legal education and at the University of California at San Diego Extension and has been a guest lecturer at the University of Southern California and California State University, Northridge Mr Abrams lives in North Hollywood, California, with his wife and five children Index Abandonment as real option, 576, 578, 580–582, 587, 597, 599, 606, 610, 611 Abrams, Jay B economic components model See Economic components model (ECM) (Abrams) log size model, 176, 177, 215 See also Log size model Academic studies on control premiums Bargeron, Schlingemann, Stulz, and Zutter, 275, 288, 289 Bradley, Desai, and Kim, 275, 285, 286, 289, 290, 303 corporate control research, other studies on, 287, 288 Houlihan Lokey Howard & Zukin (HLHZ), 259, 272, 275, 277, 279, 284, 291 international voting rights premium studies, 285 Lease, McConnell, and Mikkelson, 275, 277–279, 281, 283–285, 291, 292, 296 Maquieira, Megginson, and Nail, 266, 275, 285–287, 289–291, 300 Megginson, 275, 277–282, 284, 291 Menyah and Paudyal, 275, 288 overview, 247, 275, 289, 290 Schwert, 250, 275–277, 285, 287, 303, 324, 325, 336, 337, 359 Accounting equation, 11–15 Accrual method reporting, 7–10, 27 Acquisition premium See also Control premium academic research, 275, 276, 279–281, 289 components of, 296–301 control versus minority, 289, 290, 296 Mergerstat data, 259, 260 performance improvements, 289, 296 qualitative professional research, 267, 268, 271–273 and synergies, 289, 290, 292, 296, 297 and voting rights, 296 See also Voting rights premium (VRP) ADF See Annuity discount factors (ADFs) Airline industry, 580 Analysis of variance (ANOVA) table, 75–77 Angel investors, 516, 517 Annuity discount factors (ADFs) See also Gordon model (GM) after-tax cost of loan, calculating, 133–139 and bias in annual discounting, 113–119 definitions, 82 end-of-year cash flows, 83–91 end-of-year formulas, 94–100 equations, table of, 121 generalized Gordon model, 100 loan amortization, 82, 100, 120, 129–135 loan payments, calculating, 82, 107, 108 midyear cash flows, 91–93 midyear formula, 100, 101 monthly cash flow calculations, 114, 115, 141–143 overview, 2, 81, 90, 91, 119–121 periodic perpetuity factors (PPFs), 82, 91, 101–107 present values, 2, 81–91, 95–99, 101–110, 115–121, 123–140 principal amortization, calculating, 82, 107, 133, 135, 136, 139 sensitivity analysis, 86, 118–120 starting periods other than year one, 93–101 stub periods (fractional years), 82, 119–121, 123–130 time, denoting, 83 uses of, 81, 82 623 624 Arithmetic mean See Means, arithmetic and geometric Aschwald, Kathryn F., 305, 347 See also Columbia Financial Advisors, Inc (CFAI) Autocorrelation (serial correlation), 69, 182, 232, 233 Automobile industry, 579, 580 Balance sheet and cash flow derivation, 1, 9–13, 15, 16, 23, 25, 27 and measuring dilution in ESOPs, 470, 471 Bargeron, Schlingemann, Stulz, and Zutter, 275, 288, 289 BAS See Bid-ask spread (BAS) model (Kasper) Benchmarks for payout ratio, 35, 36 Beta in CAPM discount rate calculation, 176, 181, 186, 191, 198, 199, 215, 221 and heteroscedasticy, 191 return versus beta, 158 sum beta, 181, 182 Bias See Expert bias Bid-ask spread, 298, 400 Bid-ask spread (BAS) model (Kasper), 249, 288, 304, 305, 358 Binomial distributions and testing for expert bias, 431–434 BizComps, 69, 304, 384 Black-Scholes option pricing model (BSOPM), 250, 251, 305, 309, 311–313, 315, 318–321, 324, 358 Blockage discount, 298, 300 Blockage premium, 301 Bolotsky, Michael J., 258, 259, 267–270, 272, 294–295 Bradley, Desai, and Kim, 275, 285, 286, 289, 290, 303 Build-up method, 198, 221, 237, 246 See also Capital asset pricing model (CAPM) Buyouts dilution, sharing, 503–506 dilution in FMV, 500–503 loans, 499–503, 505 overview, 449, 499, 506 pre- and post-transaction valuations, 499–501 Index C corporations payout ratio guesstimates, 35, 36 sale to C corporation ESOP, 479–484, 490–494 Capital asset pricing model (CAPM) automated iterative approach using Newton’s method, 203–205 beta, 181, 182 and confidence intervals, 406–410, 422 discount rate calculation, 176, 181, 186, 198, 199, 215, 221 and equity valuation method, 237, 240, 245 and heteroscedasticity, 191 and invested capital approach, 244, 245 and log size model, 237, 246 obsolescence of, 181, 237 overview, 146, 147, 198, 199, 221 and privately-held companies, 221 and small companies, 199, 221, 222 and valuation errors, 421 weighted average cost of capital (WACC), 237, 243–246 Capital expenditures, 33–43 CAPM See Capital asset pricing model (CAPM) CARs See Cumulative abnormal returns (CARs) Cash flows adjustments to, 7–10, 18, 20, 23, 24, 26 cash flow equation, 33 forecasting See Forecasting cash flow gross cash flow, 31, 32, 43, 44 mathematical derivation See Mathematical derivation of cash flow and net income, 1, 7–10, 12, 14, 15, 17–22, 24–27, 33 net present value, 90, 93, 106, 107, 115, 125 and payout ratios See Payout ratio (POR) present value, 81–91, 95–99, 101–106, 115–121, 123–140 timing of, 83 Cash method reporting, 7, Cash required, 12, 23–26 Causal variables, 47 Certified Risk Analyst (CRA), 579, 599 Columbia Financial Advisors, Inc (CFAI), 305, 346–348, 354, 355 Competitive bidding, 276, 277, 324 Computer industry, 580 Index Confidence intervals and capital asset pricing model (CAPM), 406–410, 422 regression analysis, 54, 57–63, 67, 73, 406 Conglomerate buyers, 263, 265 Conglomerate mergers, 286, 287, 289–291 Control premium See also Acquisition premium academic studies on, 274–296 and acquisition premium, 296–298, 300, 301 and calculating discount for lack of control, 266 in ESOP sales, 479, 481, 483, 490, 491, 493 levels of value (LOV) charts, 257–259 Mergerstat data, 259–267, 272, 290, 293, 297–299, 303 overview, 249, 257, 358 prior qualitative professional research, 266–274 and voting rights, 274–285, 291–296, 358 Correlation in regression analysis, 52, 54, 69, 77 Cost accounting, 425, 437, 444 See also Damage calculations for manufacturers Cost approach, 586 Cost of equity model See Fama-French (FF) three-factor cost of equity model Costs and expenses, forecasting, 47–52, 54, 55, 57, 58, 63, 64, 68 Cumulative abnormal returns (CARs), 266, 275, 276, 285–290, 300 Current liabilities, 11, 13–24 Damage calculations for manufacturers assumptions, modifying to fit facts, 446, 447 cost accounting, 425, 437, 444 damage calculations, 438–445 data, lack of, 437, 443, 445 lost inventory, 437–444 lost profits, 437–445 lost profits formulas for lost sales on inventory never produced, 445, 446 lost sales, 437, 438 overview, 425, 437, 438, 448 Damage calculations for wholesale and retail business, 437, 447, 448 Data, lack of damage calculations, 437, 443, 445 regression analysis, 63 625 Data set, regression analysis, 62, 63, 70 Debt, long-term, 32–36, 42, 43 Debt restructuring study, 507, 521–533 Debt-to-equity ratio, 237 Decision tree analysis and valuation of startups, 507, 513, 514, 521–533 Decision-making See Real options analysis Delay to sale, 250, 287, 316–324, 327, 336 Dependent variable, regression analysis, 47, 51, 52, 54, 56, 66, 72 Depreciation and cash flow, 1, 8, 9, 11–26, 31–34 and payout ratio, 35–43 Dilution in buyouts of partners and shareholders See Buyouts and ESOP valuation See ESOPs, measuring and apportioning dilution Direct method for reporting cash flows, 8, Discount for lack of competition, 277, 324, 325 Discount for lack of control (DLOC) adjusting for as part of valuation process, 257, 379, 406 and ambiguity aversion, 317 calculating, 266 and control premium, 266 in ESOP sales, 480–486, 490, 493 in First Chicago approach for valuing startups, 517, 520 and foreign company data, 292 level of values (LOV) charts, 257–259, 267 overview, 249 prior academic research, 274–299 prior qualitative research, 267–274 and valuation error and uncertainty, 423 in venture capital pricing approach, 520 Discount for lack of marketability (DLOM) adjusting for as part of valuation process, 257, 379, 406 and ambiguity aversion, 317 bid-ask spread model See Bid-ask spread (BAS) model (Kasper) economic components model See Economic components model (ECM) (Abrams) in ESOP sales, 480–482, 484–486, 490–494 in First Chicago approach for valuing startups, 517, 520 mathematical formulas, 365–373 overview, 249–251, 257, 301, 358, 359 prior academic research, 274–299 626 Discount for lack of marketability (DLOM) (Continued ) prior qualitative research, 267–274 quantitative marketability discount model See Quantitative marketability discount model (QMDM) (Mercer) quantitative models, 301 restricted stock discounts, 250, 251, 305–316, 318–321, 324, 352–358 and valuation error and uncertainty, 423 in venture capital pricing approach, 520 Discount rates arithmetic versus geometric means, 230–232 See also Means, arithmetic and geometric capital asset pricing model (CAPM) See Capital asset pricing model (CAPM) and log size model See Log size model uncertainty, measuring, 405–410 and valuation error, 13, 411, 412, 414, 416–423 Discounted cash flow analysis (DCF) company-specific adjustments, 175, 176, 195, 196, 199, 214, 215, 219–222 Discounted cash flow (DCF) adjusting for independent variable, 180, 216 advantages and disadvantages of versus real options analysis, 587–593 bias, testing for, 432–434 company-specific adjustments, 214, 215 and control premiums, 300 and forecasting cash flow See Forecasting cash flow iterative process, example, 172–176 log size model example, 213–215 versus net income, 180 private companies, 187 versus real option approach, 576, 583, 584 regression analysis, use of, 47–51 and startups, valuation of, 514 strengths and weaknesses of, 196, 197, 219, 220 and traditional valuation approaches, 585–587 use of in income approach, 31 valuation process, 379, 406 Discounted time to market model, 301, 305 Discounted time to market model (Kasper), 301, 305 Index Dividends and cash flow calculations, 8, 12, 14, 18–20, 22, 24, 25, 31–33 payout ratio See Payout ratio (POR) privately-held companies, 33 DLOC See Discount for lack of control (DLOC) DLOM See Discount for lack of marketability (DLOM) Dobner, Michael, 113 Done Deals, 69 Durbin-Watson test, 69 Earnings before interest, taxes, depreciation and amortization (EBITDA), 31, 32, 440, 445–446 Earnings before interest and taxes (EBIT), 31, 32, 243 Earnings before interest but after taxes (EBIBAT), 243, 245 ECM See Economic components model (ECM) (Abrams) Economic components model (ECM) (Abrams) calculation of DLOM, 336–338, 387–399 delay to sale (component #1), 250, 287, 316–324, 327, 336, 387–389, 393–399 empirical testing of, 375, 379, 380, 386–401 monopsony power (component #2), 250, 316, 324, 325, 327, 336, 359, 391–399 overview, 250, 316, 358, 359 and quantitative marketability discount model, 338–352 support for, 338 transaction costs (component #3), 250, 325–336, 359, 365, 367–369, 373, 379, 387, 389–400 Empirical testing of economic components model calculation of DLOM, 380, 387–399 conclusion, 386 interpretation of error, 400, 401 overview, 375, 379 Empirical testing of log size model conclusion, 386 interpretation of error, 400, 401 log size equation for IBA data, 380, 381, 832 overview, 375, 379 reconciliation to IBA database, 382–386 valuation process, 379 Index Employee stock ownership plans (ESOPs) dilution, measuring and apportioning See ESOPs, measuring and apportioning dilution loans See ESOP loans selling to versus outside buyer See ESOPs, selling to versus third party Equity transactions, 12, 14–19, 22, 26 Equity valuation method, 237–243 ESOP loans annuity discount factors, use of in determining present value, 2, 82 and dilution, 453, 460, 466–468, 471–474 fairness opinions, 473, 474 function of, 470 and sale to ESOP versus selling to third party, 480, 483, 490, 491, 493, 494 ESOPs, measuring and apportioning dilution absolute dilution, 454 apportioning dilution, 450, 453, 454, 457, 463–466, 470–474, 476 benefits of, 469, 470 comparative static analysis of dilution equations, 475, 476 dilution to ESOP (type 1), 453–455, 458–461, 464, 465, 469, 470, 475, 476 dilution to seller (type 2), 454, 455, 461–465, 469, 470, 475, 476 direct approach, 457–466, 469 ESOP loans, effect of, 453, 460, 466–468, 471–474 formulas, application of, 470 iterative approach, 466–469 legal issues, 473, 474 lifetime ESOP costs, calculation of, 456, 457 mathematical terms defined, 455, 456 nonselling owners, dilution to, 472, 473 overview, 449, 450, 453, 454 partial sales, 474 pre-transaction value, 453–455, 457, 466–473 relative dilution, 454 types of dilution, 454, 455 ESOPs, selling to versus third party advantages and disadvantages of, 480, 481 assumptions and changes, importance of, 494 breakeven percentage, calculating, 479, 485, 486, 488–490, 492–494 627 calculations, 486–494 and ESOP loans, 480, 483, 490, 491, 493, 494 ESOP premium, 480–482, 484, 486, 487, 490, 492–494 mathematical terms defined, 480, 481 overview, 479 personal capital gains tax, 481, 482, 485, 490, 491, 493 sale of firm to third party (maintaining S corporation), 479–482, 484, 485, 490–494 sale to C corporation ESOP, 479–484, 490–494 shareholder wealth calculations, 487–491 total wealth of owner after personal taxes, 485, 486, 491 Estimation formula for payout ratio benchmarks for payout ratio, 35, 36 capital expenditures over depreciation, 36–42 Exit price, 300 Expert bias detecting, 430–432 and discounted cash flow valuation, 432–434 overview, 425, 429, 434 and selection of guideline companies, 429–432 Exponentially declining sales growth model, 508, 514, 534–536 Fairness opinions, ESOP loans, 473, 474 Fama, Eugene F., 151, 152, 166, 167, 181, 184–187 Fama-French (FF) three-factor cost of equity model, 151, 182–184, 187 Fermi, Enrico, 542 Financial buyers, 272 Financial crisis of 2008, 156, 159, 162, 166, 167 Financing activities, 8, 9, 18–20, 22, 24, 26, 27 First Chicago approach for valuing startups advantages of, 519, 520 and capital structure changes, 515 discount for lack of control, 517, 520 discount for lack of marketability, 517, 520 and discounted cash flow analysis, 514 discounting forecasted cash flow versus net income, 514 628 First Chicago approach for valuing startups (Continued ) example, 517, 518 origin of, 514 overview, 507, 513, 514 scenarios, 514, 517, 518 and venture capital rates of return, 515–517 Fixed assets, 8, 9, 12, 17, 18 See also Property, plant, and equipment (PP&E) FMV Opinions (FMVO), 251, 305, 352, 356–358 Forecasting cash flows See Forecasting cash flow costs and expenses, 47–52, 54–55, 57–58, 63–64, 68 and Monte Carlo simulation, 541–543 See also Monte Carlo risk simulation and risk analysis methods, 541 sales, 47–52, 64–68 Forecasting cash flow annuity discount factors See Annuity discount factors (ADFs) and calculating economic damages, 425 See also Damage calculations for manufacturers difficulties in, 31, 32 forecasting net income compared, 514 Gordon Model See Gordon Model (GM) gross cash flow, 31, 32, 43, 44 mathematical derivation of cash flow See Mathematical derivation of cash flow overview, 1–3 as part of valuation process, 10, 379, 406 payout ratio See Payout ratio (POR) regression analysis See Regression analysis Fowler, Bradley, 507, 514, 515, 520 Fractional interests, 352 French, Kenneth R., 151, 152, 166, 167, 181, 184–187 Geometric mean See Means, arithmetic and geometric Glass, Carla, 273, 290, 298 Glass and McCarter, 273, 290, 298 Golder, Stanley C., 514 Gordon model (GM) constant forecast growth, 72, 81, 82, 112, 113, 119 definitions, 111 Index discount rate in log size model, computation of, 172 end-of-year assumption, 83–85, 87–90, 100–102, 114, 115, 119 end-of-year multiple, 82, 88, 89, 143 generalized, 100–102 and Ibbotson’s total return equation, 193, 217 midyear assumption, 81, 83, 125 midyear cash flows, 91–93, 114 midyear multiple, 81, 82, 92, 93, 100–102, 112, 121 monthly annuity discount factor, 114, 115, 141–143 multiple, 81, 82, 85–89, 92, 93, 95, 96, 98–102, 112, 121, 143, 220, 231, 232 overview, 81, 82, 121 and periodic perpetuity factors (PPFs), 101, 102, 105, 118, 119 and price/earnings (P/E) ratio, 91, 110–113, 121 and price/sales (PS) ratio, 110, 111, 113 relationship with ADF, 89, 90 as special case of ADF, 88, 89 use of, 87 valuation using Newton’s iterative process, 204, 205 Grabowski, Roger, 145, 152, 156, 176, 181, 188–191, 212, 215, 307 Growth rates and payout ratios, 36 and valuation error, 410, 411, 414–423 Growth stocks versus value stocks, 182–187 Guideline companies (GCs) foreign companies, 292 PE multiples, 112, 113 privately-held companies, 258, 270 regression analysis, 47, 69–73, 198 selection of and expert bias, 429–432 sources of, 69 Guideline merger and acquisition method (GMAM) acquisition premiums, 267, 268 bias in selection of guideline companies, 429–432 control premiums, 275, 277, 291, 300, 301 and regression analysis, 47, 69–73, 198, 216, 221, 222 selection of guideline companies, 430 strengths and weaknesses of, 219, 220 and synergies, 274 Index Guideline public company method (GPCM) and annuity discount factors, 82 bias, testing for, 429–432 and control premiums, 258, 290, 291, 300 PE multiples, 112, 113, 220 privately-held companies, 198, 221, 258, 270 and regression analysis, 47, 69–73, 198, 199, 216, 221, 222 and Revenue Ruling 59-60, 196–198, 219 selection of guideline companies, 429, 430 and size of company, 181, 198, 199, 219–222 strengths and weaknesses of, 219, 220 Harrison, Paul, 145, 162, 164–167 Heteroscedasticity, 71–73, 191, 197, 220 High-tech and e-business, 576, 579, 581 Historical stock returns analysis of, 152–158 data selection, 162–167 Fama-French three-factor multiple regression model, 151 and financial crisis of 2008, 159–162 market performance, 159–162 return versus beta (regression #3), 158 return versus log size (regression #2), 156–159, 162–164 return versus standard deviation of returns (regression #1), 155, 156, 159, 162–164 Horizontal buyers, 261, 263, 265, 266 Houlihan Lokey Howard & Zukin (HLHZ), 259, 272, 275, 277, 279, 284, 291 IBA database, 63, 69, 304, 338, 375, 379, 380, 382–387, 389, 390, 392, 400 Ibbotson, Roger G., 145, 146, 160–162, 165–167, 169, 173, 181, 182, 184, 190, 193, 199, 213, 217, 221, 226, 227 Ibbotson Associates, SBBI valuation yearbooks See Stocks, Bonds, Bills and Inflation (SBBI) yearbooks Income approach, 31, 44, 586 Income statement, 1, 8–11, 13–15, 17, 25, 27 Independent variables in regression analysis, 47, 51, 52, 54, 56, 59–63, 65–68, 72, 77 Indirect method for reporting cash flows, 8–11, 22 Indro, Daniel C., 232, 233 629 Institute of Business Appraisers (IBA) database See IBA database Internal rate of return (IRR), 515–517 Internal Revenue Code (IRC) S corporation taxation, 479 section 1042, rollover tax advantage for C corporation ESOPs, 479, 480, 490 Inventory, damage formulas See Damage calculations for manufacturers Invested capital approach, 243–245 Investing activities, 8, 9, 18–20, 22, 24, 26, 27 Investment risk See Risk Iterative approach for CAPM, automating, 203–205 Iterative valuation approach equity valuation method, 237–243 invested capital approach, 243–245 and log size model, 245 overview, 237, 245, 246 Jankowske, Wayne, 267, 270–272, 295, 317 Kasper, Larry J., 288, 301, 304, 305, 358 bid-ask spread (BAS) model, 249, 288, 304, 305, 358 King, David, 152, 156, 176, 181, 188–191, 212, 215, 307 Koeplin, Sarin, and Shapiro, 304 Large companies, confidence intervals and measuring valuation uncertainty, 406–410 Lease, McConnell, and Mikkelson, 275, 277–279, 281, 283–285, 291, 292, 296 Lee, Wayne Y., 232, 233 Levels of value (LOV) charts, 257–259 Litigation damage calculations See Damage calculations for manufacturers; Damage calculations for wholesale and retail business expert witnesses, detecting bias of See Expert bias Loans after-tax cost of loan, calculating, 133–139 amortization, 82, 100, 120, 129–135 buyouts of partners and shareholders, 499–503, 505 employee stock option plans (ESOPs) See ESOP loans payments, calculating, 82, 107, 108 present value of, 2, 82, 91, 107–110 630 Log size model application of, 167–180 benefits of, 146 and CAPM, 221 See also Capital asset pricing model (CAPM) and company size, 151, 152, 187, 188 confidence intervals, 146, 164, 406–410 discount rates, 167–172, 177, 180, 187–191, 193–196, 198, 221, 230–232 empirical testing of See Empirical testing of log size model example of iterative process, discounted cash flow analysis, 172–176 Grabowski and King results, 145, 152, 176, 181, 188–191, 215, 307, 308 historical equity return correlation, 187, 188 historical stock returns, analysis of, 152–167 industry effects, 191, 192 and iterative valuation approach, 245 mathematics, 207–210 overview, 145, 146, 198, 199, 221, 222 privately-held companies, 187–191, 193–196, 198, 221 public companies, 192, 193 Revenue Ruling 59-60 requirements for guideline public companies, 196–198, 219 summary, 211–222 total return versus equity premium, 176, 177 Long-term debt (LTD) and payout ratio, 32–36, 42, 43 Lost profits See Damage calculations for manufacturers Lotus 123 See also Spreadsheets natural logarithms, 155 regression analysis tools, 2, 66, 67 See also Regression analysis Management Planning, Inc (MPI), restricted stock discount data, 250, 251, 305–308, 312, 315, 316, 319–323, 338–341, 347–350, 352–358 Manufacturers, damage calculations for See Damage calculations for manufacturers Maquieira, Megginson, and Nail, 266, 275, 285–287, 289–291, 300 Index Market methods, 2, 219, 220, 429, 586 See also Guideline merger and acquisition method (GMAM); Guideline public company method (GPCM) Markup period, 275, 276 Mathematical derivation of cash flow algebraic symbols used, 11, 12 cash required, adjusting for, 23–25 comparison to other cash flow definitions, 25, 26 dynamic equation, 11, 13–15 equity transactions, 18–20 income statement, bridge to, 14, 15 income statement and statement of cash flows as reconciliations, 27 overview, 1, 7–11 property, plant, and equipment transactions, analysis of, 15–18 static equation, 12 working capital required, 21–23 McCarter, Mary M., 273, 290, 298 Means, arithmetic and geometric arithmetic mean superiority, 226–232 converting geometric to arithmetic mean, 226 difference between means, 226 Indro and Lee article, 232, 233 mathematical definitions, 225, 226 overview, 146 prior literature, 226 Megginson, William L., 275, 277–282, 284, 291 See also Maquieira, Megginson, and Nail Mercer, Z Christopher, 81, 120, 249, 250, 267–269, 298, 305, 358 Management Planning study, 305 modified traditional levels of value chart, 258 quantitative marketability discount model See Quantitative marketability discount model (QMDM) (Mercer) research on control premiums, 272–274, 290 restricted stock sales, 305, 315, 316, 319, 358 Mergers and acquisitions guideline company method See Guideline merger and acquisition method (GMAM) and real options analysis, 576, 581, 582 Mergerstat, control premium data, 259–267, 272, 290, 293, 297–299, 303 Index Microsoft Excel See also Spreadsheets natural logarithms, 155 regression analysis tools, 2, 66, 68 See also Regression analysis and SLS Excel Solution, 598, 599, 611–613 and use of Risk Simulator See Monte Carlo risk simulation Miles, Raymond C., 379, 384, 400 Miller, Warren D., 180, 199, 215, 222 Modeling Risk: Applying Monte Carlo Simulation, Real Options, Portfolio Optimization and Stochastic Forecasting (Mun), 508, 541, 593 Monopsony power, 250, 316, 324, 325, 327, 336, 359, 391–399 Monte Carlo risk simulation confidence intervals, 554–556 distributional fitting, 567–571 forecast charts, use of, 554–556 and Microsoft Excel, 543, 546, 547, 552, 571 overview, 541–543 Risk Simulator, trial license software, 571 Risk Simulator, use of, 541, 543, 546–556 sensitivity analysis, 563–567 spider charts, 558, 559, 561–563, 566 tornado analysis, 556–563 and traditional approaches to risk and uncertainty analysis, 541–545 Monte Carlo simulation (MCS) overview, 508, 541–543 risk simulation using Risk Simulator See Monte Carlo risk simulation uses of, 542 Moskowitz-Vissing-Jorgensen guesstimate for payout ratios for privately-held companies, 35, 36 Mun, Jonathan, 508 Myers, Stewart C., 233, 515–517 Nath, Eric, 267–270, 272–274, 294, 300 Net cash flow, 8–10, 22, 25, 26 Net income and cash flow, 1, 7–10, 12, 14, 15, 17–22, 24–27, 33 converting forecast net income to forecast cash flows See Payout ratio (POR) discounting forecasted net income, 31, 32 versus forecasted cash flow, 514 and payout ratio, 33, 34, 42–44 See also Payout ratio (POR) 631 Net present value (NPV) cash flow, 90, 93, 106, 107, 115, 125 discount to as part of valuation process, 379, 406 Net working capital See Working capital Newton, Isaac, 203 Noise, 184, 185 Non-cash expenses, 18, 21, 22, 25, 26 See also Depreciation Nonconglomerate mergers, 286, 287 Oil and gas industry, 576, 579, 580 OLS See Ordinary least squares (OLS) Operating activities, 7–9, 14, 18, 20–22, 24–27 Ordinary least squares (OLS) and heteroscedasticity, 191 overview, regression analysis, 48, 51, 52, 56, 71 Other current assets (OCA), 11, 13–22, 24 Overvaluation, 32, 173, 187, 198, 199, 214, 221, 222, 267, 270, 411, 414, 421, 443, 514 Partners, buyouts of See Buyouts Partnership Profiles database, 63, 68 Payout ratio (POR) benchmarks, 35, 36 cash flow equation, 33 defining cash flow through, 33, 34 estimation formula (equation 2.24), 35–44 exact equations for (equations 2.8 and 2.9), 34, 35, 42–44 and forecasting cash flow, problems with, 31, 32 and gross cash flow, 43, 44 and long-term debt, 32–36, 42, 43 mathematical symbols used, 32 and net income, 33, 34, 42–44 and net working capital, 32–36, 42, 43 overview, 1, 31, 44 required net working capital and long-term debt, increase in, 42 and retention ratio, 32, 34, 35 Periodic perpetuity factors (PPFs), 82, 91, 101–107 Pharmaceutical industry research and development, 576, 579, 581, 592 Plummer, James L., 514, 520 Pratt’s Stats, 63, 69, 304 632 Premiums control premium See Control premium for discounted forecast net income, 32 privately-held companies, 176, 177, 180, 215 risk premium See Risk premium S corporation premium in ESOP sales, 480, 481, 485, 491, 493, 494 Present value factor, 84, 89, 102, 104, 108, 115, 118, 119, 121, 127–130, 138 Present value (PV) See also Net present value (NPV) cash flows, 81–91, 95–99, 101–106, 115–121, 123–140 See also Annuity discount factors (ADFs) loans, 2, 82, 91, 107–110 Price-to-cash flow (P/CF) multiples and empirical testing of Abrams’ valuation theory, 375, 382, 383, 385, 386, 400 See also Empirical testing of economic components model; Empirical testing of log size model Price-to-earnings (PE) ratio Gordon model, 110–113, 121 PE multiple, 169, 181, 183, 188, 197, 198, 220 reconciling IBA PE multiples and Abrams’ valuation theory P/CF multiples, 379, 383, 392, 400 See also Empirical testing of economic components model; Empirical testing of log size model regression analysis, 181 Price-to-sales (PS) ratio Gordon model, 110, 111, 113 overview, PS multiple, 181, 198 regression analysis, 181 Private firm risk (PFR), 180, 193–197, 215–219 Privately-held companies See also Small companies and CAPM, 181, 182, 221 and control premiums See Control premium discount for lack of control See Discount for lack of control (DLOC) discount for lack of marketability See Discount for lack of marketability (DLOM) discount rate, 152, 156, 177, 180, 186–196, 198, 209, 218, 220, 221 discounted cash flow analysis, 196, 197, 213, 214, 219 Index dividends, 33, 35 See also Payout ratio (POR) Fama-French three-factor model for calculating discount rate, 182, 183 and growth versus value stocks, 183, 186, 187 guideline company data, 69, 258, 292 and guideline public company method, 181, 198, 219–221, 270 See also Guideline public company method (GPCM) and log size model for calculating discount rates, 187–191, 193–196, 198, 221 Moskowitz-Vissing-Jorgensen guesstimate for payout ratios, 35, 36 overvaluation, 198, 199, 221, 222 payout ratios, 35 See also Payout ratio (POR) premium for, 176, 177, 180, 215 private firm risk (PFR), 180, 193–197, 215–219 rate of return, 192, 193 return versus log size (regression #2), 156, 164, 207–209, 212, 213 return versus standard deviation of returns (regression #1), 156 risk, 193–197, 217–219 Probabilistic methods of valuation Monte Carlo risk simulation See Monte Carlo simulation (MCS) real options See Real options analysis startup companies See Startups, valuation of Probabilistic scenarios, 543, 544 Property, plant, and equipment (PP&E), 8, 12–18, 20–26 Purpose of valuation, 300 Put option model quantitative marketability discount model compared, 315, 316 regression model compared, 312–315 use of to calculate DLOM of restricted stock, 308, 309 See also Black-Scholes option pricing model (BSOPM) QMDM See Quantitative marketability discount model (QMDM) (Mercer) Qualitative professional research on control premiums Bolotsky, Michael J., 258, 259, 267–270, 272, 294–295 Glass and McCarter, 273, 290, 298 Index Jankowske, Wayne, 267, 270–272, 295, 317 Mercer, Z Christopher, 272–274, 290 Nath, Eric, 267–270, 272–274, 294, 300 overview, 266, 267, 273, 274 Roach, George P., 271–273, 286, 289 Quantitative marketability discount model (QMDM) (Mercer) and annuity discount factor, 81, 82 criticism of, 301, 343–352, 355, 356 described, 301–304 holding period for, 301 Koeplin, Sarin, and Shapiro research, 304 overview, 249, 250, 258, 259, 358 rebuttal to criticisms of, 338–343, 345 and restricted stock discounts, 305, 315, 316, 319, 358 R value, 52, 54 r value, 52, 54 Rates of return in First Chicago approach, 517, 518, 520 venture capital, 515–517, 520, 521 Real estate, 581 Real options analysis abandonment, 576, 578, 580–582, 587, 597, 599, 606, 610, 611 acceptance of, 582, 583 criticisms of, 584, 585 and decision-making process, 576, 578–580, 583, 584, 593 discounted cash flow analysis compared, 588, 590–593 and financial options, 594–597 implementing real options analysis, 578, 579 industries using, 579–581 in mergers and acquisitions valuations, 581, 582 overview, 508, 509, 575–578 prerequisites for real options analysis, 583, 584 Real Options Super Lattice Solver software, use of, 597–616 and traditional valuation approaches, 585–597 and uncertainties, 576, 577, 582, 584, 588 Real Options Analysis: Tools and Techniques, 2nd ed (Mun, 2006), 508, 509, 541, 575, 579, 593, 596, 598–599 633 Real Options Analysis Toolkit, 599, 600 Regression analysis analysis of variance (ANOVA) table, 75–77 causal variables, 47 confidence intervals, 54, 57–63, 67, 73, 406 correlation, 52, 54, 69, 77 costs and expenses, forecasting, 47–52, 54, 55, 57, 58, 63–64, 68 data, missing or insufficient, 63 data set, 62, 63, 70 dependent variable, 47, 51, 52, 54, 56, 66, 72 in discounted cash flow analysis, 47–51 and guideline company methods, 47, 69–73, 216, 221, 222 historical stock returns, 152–168 independent variables, 47, 51, 52, 54, 56, 59–63, 65–68, 72, 77 mean of a and b, 54, 55 ordinary least squares (OLS), 48, 51, 52, 56, 71 overview, 1, 2, 47, 48, 73, 74 R value, 52, 54 r value, 52, 54 regression equation, selecting, 62, 63 regression statistics, testing relationship between variables, 52–63 sales, forecasting, 64–68 spreadsheet tools, 47, 48, 66–68, 75 spurious correlation, 54, 68 standard error of y-estimate, 54, 57, 60–63, 67, 72, 74 t-distribution, 57–61 time series analysis, 69 uses of, 47 variance of a and b, 55–57, 62 weighted least squares (WLS), 71 z-distribution, 57, 58, 60 Required cash, 12, 23–26 Restricted stock discounts and discount for lack of marketability, 250, 251, 305–316, 318–321, 324, 352–358 Retention ratio (RR), 32, 34, 35 Return versus log size (regression #2), 156–159, 162–164, 169, 172–175, 190, 212, 213 Return versus standard deviation of returns (regression #1), 155, 156, 159, 162–164, 208, 211, 212 Revenue Ruling 59-60, 196–198, 219 634 Risk and company size, 181, 183, 189, 191, 199, 209–211, 222 company-specific, 195, 196, 217, 219 private firm risk (PFR), 180, 193–197, 215–219 and return, 152, 155, 158, 159, 162, 183 simulation See Monte Carlo risk simulation systematic, 186 unsystematic, 180, 215 Risk premium equity risk, 161, 176, 205, 215, 238, 240 private firms, 180, 193–197, 215, 217–219 small firms, 221 Risk Simulator software features of, 556–571 system requirements, 571 trial license, obtaining, 571 use of, 541, 543–556 Risk-free rate, 152, 156, 176, 177, 191, 207, 208, 212, 215, 238, 240 Roach, George P., 271–273, 286, 289 Robert Morris Associates (RMA), 180, 199, 216, 222 Runup period, 275, 276 S corporations payout ratio guesstimates, 35, 36 premium in ESOP sales, 480, 481, 485, 491, 493, 494 sale of to third party versus ESOP, 479–482, 484, 485, 490–494 Sales, forecasting, 47–52, 64–68 SBBI See Stocks, Bonds, Bills and Inflation (SBBI) yearbooks (Ibbotson Associates) Scenario analysis, 541, 543, 544 Schwert, G William, 250, 275–277, 285, 287, 303, 324, 325, 336, 337, 359, 389, 391–399 Sensitivity analysis annuity discount factors (ADFs), 86, 118–120 risk simulation, 542–544, 563–567 startups, valuation of, 508, 513, 514, 534, 536 and tornado analysis, 556–566 SFAS No 95, “Statement of Cash Flows,” Shareholders, buyouts of See Buyouts Shareholders’ equity, 11–14, 18, 19, 23, 25, 26 Index Size of company See also Small companies and capital asset pricing model (CAPM), 181, 182 and discount rates based on arithmetic versus geometric means, 230 and empirical testing of Abrams’ valuation theory See Empirical testing of economic components model; Empirical testing of log size model and Fama-French three-factor model, 182 and growth-versus-value stocks, 183–186 and guideline public company method (GPCM), 181, 198, 199, 219–222 and log size model, 151, 152, 187, 188 and relationship to price/earnings (P/E) multiples, 379, 383 Small companies See also Privately-held companies arithmetic versus geometric mean returns, 146, 230, 231 See also Means, arithmetic and geometric and CAPM, 199, 221, 222 confidence intervals and measuring valuation uncertainty, 410 empirical testing of Abrams’ valuation theory See Empirical testing of economic components model; Empirical testing of log size model and guideline public company method, 181, 196–198, 219–222 iterative approach, use of, 245 leverage, 186 and log size model, 146, 379 See also Log size model overvaluation, 198, 199, 221, 222 rates of return, 151, 181, 182, 191, 192, 210–212 and Revenue Ruling 59-60, 196 risk, 159, 210 SPARC system, 180, 199, 215, 222 Spreadsheets analysis of variance, 75–77 automating iteration, 203–205 and decision tree analysis, 522 Lotus 123, 2, 66, 67 Microsoft Excel, 2, 66, 68, 598, 599, 611–613 See also Monte Carlo risk simulation natural logarithm formulas, 155 regression analysis, 47, 48, 65–68, 75–77 sales, forecasting, 65–68 and statistics packages, 68 635 Index Spurious correlation, 54, 68 Standard error of y-estimate, 54, 57, 60–63, 67, 72, 74 Startups, valuation of and capital structure changes, 515 debt restructuring study, 507, 521–533 decision tree analysis, 507, 513, 514, 521–533 and discounted cash flow analysis, 514 discounting forecasted cash flow versus net income, 514 exponentially declining sales growth model, 508, 514, 534–536 First Chicago approach, 507, 513–520 multiple-scenario approach, 514 overview, 507, 508, 513, 514 and sensitivity analysis, 508, 513, 514, 534, 536 top-down approach, 508, 534 uncertainty, 513, 519 venture capital pricing approach, 507, 513, 520, 521 Statement of cash flows, 7, 10, 11, 13, 15, 17, 20, 22, 24, 25, 27 Sterling Freight Lines, Inc v Prairie Material Sales, Inc., 447, 448 Stock cash returns on, 31 dilution of See Buyouts; ESOPs, measuring and apportioning dilution dividends See Dividends growth versus value stocks, 182–187 historical returns See Historical stock returns purchase and sale of, 12, 14, 18–20, 22, 24, 26 repurchase, restricted See Restricted stock discounts and discount for lack of marketability treasury stock, 12, 13, 18–26 Stockholders’ equity See Shareholders’ equity Stocks, Bonds, Bills and Inflation (SBBI) yearbooks (Ibbotson Associates), 31, 146, 152, 159, 160, 166, 168, 182–184, 192, 205, 216 Strategic buyers, 260–262, 264–267, 272, 274, 300 Student’s t-distribution, 57–61 Sum beta, 181, 182 Super Lattice Solver (SLS) software CD-ROM, about, 597, 598 components of, 598–600 downloads and getting started videos, 579, 598 Lattice Maker, 615, 616 Multinomial Lattice Solver (MNLS), 598, 599, 608–611 Multiple Super Lattice Solver (MSLS), 598, 599, 606–608 Single Super Lattice Solver (SLS), 598–605 SLS Excel Solution, 598, 599, 611–613 SLS Functions, 598, 599, 613, 614, 616 Supply-side model, 166, 167 Synergies, and acquisition premiums, 259, 260, 272, 273, 292, 300 t-distribution, 57–61 Telecommunications industry, 579, 580 Time series analysis, 69 Tornado analysis, 556–563 Transaction costs, 250, 325–336, 359, 365, 367–369, 373, 379, 387, 389–400 Trout, Robert, 113, 114, 143 Troy’s Almanac, 180, 199, 216, 222 Uncertainty and risk, 575, 576 See also Real options analysis and startups, valuation of, 513, 519 traditional approaches to risk and uncertainty analysis, 541–545 See also Monte Carlo risk simulation valuation uncertainty See Valuation uncertainty Unified valuation theory, 401 Utilities industry, 579, 581 Valuation error absolute error, 411 measuring effects of, 375, 410–422 overview, 422, 423 relative error, 411 sources of, 406 uncertainty distinguished, 405 Valuation methods advantages and disadvantages of, 587–594 combined approaches, 586, 587 cost approach, 586 636 Valuation methods (Continued ) guideline companies See Guideline merger and acquisition method (GMAM); Guideline public company method (GPCM) income approach, 31, 44, 586 intangible assets, 586, 587 market approach, 2, 586 overview, 585 probabilistic methods See Monte Carlo risk simulation; Real options analysis; Startups, valuation of traditional views, 585, 586 unbiased valuation, attributes of, 429 See also Expert bias Valuation process, 379 Valuation uncertainty error distinguished, 405 measuring, 406–410 overview, 375, 405, 422, 423 sources of, 406 Value stocks, 182–187 Variables discounted cash flow, adjusting for independent variable, 180, 216 Index Monte Carlo risk simulation, 567–571 and regression analysis, 47, 48, 51–63, 65–68, 71–74 Venture capital pricing approach discount for lack of control, 520 discount for lack of marketability, 520 overview, 507, 513, 520, 521 rates of return, 515–517, 520, 521 Vertical buyers, 261, 263, 265 Vitex Manufacturing Corp v Caribtex Corp., 448 Voting rights premium (VRP), 274–285, 291–296, 358 Weighted average cost of capital (WACC), 237, 243–246 Weighted least squares (WLS), 71, 191 Working capital net working capital, 1, 9, 21, 25, 32–36, 42, 43 required working capital, 12, 21–26 www.abramsvaluation.com, 508 www.realoptionsvaluation.com, 579, 598 z-distribution, 57, 58, 60 ... of Tables and Figures Table 9.4A Table 9.6A Table 9. 4B Table 9. 6B Table 9.4C Table 9.6C Table 9.4D Table 9.6D Table 9.4E Table 9.6E Table 9.4F Table 9.6 F Table 9.4G Table 9.6G Calculation Calculation... www.wiley.com Library of Congress Cataloging-in-Publication Data: Abrams, Jay B Quantitative business valuation : a mathematical approach for today’s professionals / Jay B Abrams — 2nd ed p cm Includes.. .Quantitative Business Valuation Quantitative Business Valuation A Mathematical Approach for Today’s Professionals Second Edition JAY B ABRAMS John Wiley & Sons, Inc Copyright C 2010 by John