Title Details

Mark G. Filler, CPA/ABV, CBA, AM, CVA, is President of Filler & Associates, a valuation and litigation support practice. He recently was also chair of the editorial board of NACVA's The Valuation Examiner and coauthor of NACVA's quarterly marketing newsletter Insights on Valuation. Filler has published various articles and is recognized as a qualified expert witness, testifying frequently on business valuation, commercial damages, and personal injury matters at depositions and in state and federal courts.

James A. DiGabriele, PhD/DPS, CPA/ABV, CFF, CFE, CFSA, CR.FA, CVA, is a professor of accounting at Montclair State University and has been published in various journals, including Journal of Forensic Accounting, Journal of Business Valuation and Economic Loss Analysis, and The Value Examiner. Dr. DiGabriele is also Managing Director of DiGabriele, McNulty, Campanella & Co., LLC, an accounting firm specializing in forensic/investigative accounting and litigation support.

Preface xvii

Is This a Course in Statistics? xvii

How This Book Is Set Up xviii

The Job of the Testifying Expert xix

About the Companion Web Site—Spreadsheet Availability xix

Note xx

Acknowledgments xxi

INTRODUCTION The Application of Statistics to the Measurement of Damages for Lost Profits 1

The Three Big Statistical Ideas 1

Variation 1

Correlation 2

Rejection Region or Area 4

Introduction to the Idea of Lost Profits 6

Stage 1. Calculating the Difference Between Those Revenues That Should Have Been Earned and What Was Actually Earned During the Period of Interruption 7

Stage 2. Analyzing Costs and Expenses to Separate Continuing from Noncontinuing 8

Stage 3. Examining Continuing Expenses Patterns for Extra Expense 8

Stage 4. Computing the Actual Loss Sustained or Lost Profits 8

Choosing a Forecasting Model 9

Type of Interruption 9

Length of Period of Interruption 10

Availability of Historical Data 10

Regularity of Sales Trends and Patterns 10

Ease of Explanation 10

Conventional Forecasting Models 11

Simple Arithmetic Models 11

More Complex Arithmetic Models 11

Trendline and Curve-Fitting Models 12

Seasonal Factor Models 12

Smoothing Methods 12

Multiple Regression Models 13

Other Applications of Statistical Models 14

Conclusion 14

Notes 15

CHAPTER 1 Case Study 1—Uses of the Standard Deviation 17

The Steps of Data Analysis 17

Shape 18

Spread 19

Conclusion 23

Notes 23

CHAPTER 2 Case Study 2—Trend and Seasonality Analysis 25

Claim Submitted 25

Claim Review 26

Occupancy Percentages 26

Trend, Seasonality, and Noise 28

Trendline Test 33

Cycle Testing 33

Conclusion 34

Note 36

CHAPTER 3 Case Study 3—An Introduction to Regression Analysis and Its Application to the Measurement of Economic Damages 37

What Is Regression Analysis and Where Have I Seen It Before? 37

A Brief Introduction to Simple Linear Regression 38

I Get Good Results with Average or Median Ratios—Why Should I Switch to Regression Analysis? 40

How Does One Perform a Regression Analysis Using Microsoft Excel? 43

Why Does Simple Linear Regression Rarely Give Us the Right Answer, and What Can We Do about It? 51

Should We Treat the Value Driver Annual Revenue in the Same Manner as We Have Seller’s Discretionary Earnings? 60

What Are the Meaning and Function of the Regression Tool’s Summary Output? 68

Regression Statistics 69

Tests and Analysis of Residuals 75

Testing the Linearity Assumption 77

Testing the Normality Assumption 78

Testing the Constant Variance Assumption 80

Testing the Independence Assumption 83

Testing the No Errors-in-Variables Assumption 84

Testing the No Multicollinearity Assumption 84

Conclusion 87

Note 87

CHAPTER 4 Case Study 4—Choosing a Sales Forecasting Model: A Trial and Error Process 89

Correlation with Industry Sales 89

Conversion to Quarterly Data 89

Quadratic Regression Model 92

Problems with the Quarterly Quadratic Model 92

Substituting a Monthly Quadratic Model 94

Conclusion 95

Note 99

CHAPTER 5 Case Study 5—Time Series Analysis with Seasonal Adjustment 101

Exploratory Data Analysis 101

Seasonal Indexes versus Dummy Variables 102

Creation of the Optimized Seasonal Indexes 103

Creation of the Monthly Time Series Model 108

Creation of the Composite Model 108

Conclusion 115

Notes 115

CHAPTER 6 Case Study 6—Cross-Sectional Regression Combined with Seasonal Indexes to Determine Lost Profits 117

Outline of the Case 117

Testing for Noise in the Data 119

Converting to Quarterly Data 119

Optimizing Seasonal Indexes 119

Exogenous Predictor Variable 124

Interrupted Time Series Analysis 124

“But For” Sales Forecast 126

Transforming the Dependent Variable 130

Dealing with Mitigation 130

Computing Saved Costs and Expenses 133

Conclusion 137

Note 138

CHAPTER 7 Case Study 7—Measuring Differences in Pre- and Postincident Sales Using Two Sample t-Tests versus Regression Models 139

Preliminary Tests of the Data 139

Using the t-Test Two Sample Assuming Unequal Variances Tool 141

Regression Approach to the Problem 141

A New Data Set—Different Results 143

Selecting the Appropriate Regression Model 143

Finding the Facts Behind the Figures 148

Conclusion 151

Notes 153

CHAPTER 8 Case Study 8—Interrupted Time Series Analysis, Holdback Forecasting, and Variable Transformation 155

Graph Your Data 155

Industry Comparisons 155

Accounting for Seasonality 157

Accounting for Trend 161

Accounting for Interventions 161

Forecasting “Should Be” Sales 164

Testing the Model 167

Final Sales Forecast 169

Conclusion 169

CHAPTER 9 Case Study 9—An Exercise in Cost Estimation to Determine Saved Expenses 171

Classifying Cost Behavior 171

An Arbitrary Classification 172

Graph Your Data 172

Testing the Assumption of Significance 174

Expense Drivers 174

Conclusion 177

CHAPTER 10 Case Study 10—Saved Expenses, Bivariate Model Inadequacy, and Multiple Regression Models 179

Graph Your Data 179

Regression Summary Output of the First Model 181

Search for Other Independent Variables 183

Regression Summary Output of the Second Model 185

Conclusion 188

CHAPTER 11 Case Study 11—Analysis of and Modification to Opposing Experts’ Reports 189

Background Information 189

Stipulated Facts and Data 190

The Flaw Common to Both Experts 194

Defendant’s Expert’s Report 196

Plaintiff’s Expert’s Report 199

The Modified-Exponential Growth Curve 201

Four Damages Models 208

Conclusion 208

CHAPTER 12 Case Study 12—Further Considerations in the Determination of Lost Profits 209

A Review of Methods of Loss Calculation 210

A Case Study: Dunlap Drive-In Diner 211

Skeptical Analysis Using the Fraud Theory Approach 212

Revenue Adjustment 212

Officer’s Compensation Adjustment 214

Continuing Salaries and Wages (Payroll) Adjustment 215

Rent Adjustment 215

Employee Bonus 216

Discussion 216

Conclusion 217

CHAPTER 13 Case Study 13—A Simple Approach to Forecasting Sales 221

Month Length Adjustment 221

Graph Your Data 221

Worksheet Setup 222

First Forecasting Method 227

Second Forecasting Method 227

Selection of Length of Prior Period 228

Reasonableness Test 228

Conclusion 229

CHAPTER 14 Case Study 14—Data Analysis Tools for Forecasting Sales 231

Need for Analytical Tests 231

Graph Your Data 231

Statistical Procedures 233

Tests for Randomness 235

Tests for Trend and Seasonality 240

Testing for Seasonality and Trend with a Regression Model 246

Conclusion 249

Notes 249

CHAPTER 15 Case Study 15—Determining Lost Sales with Stationary Time Series Data 251

Prediction Errors and Their Measurement 251

Moving Averages 252

Array Formulas 254

Weighted Moving Averages 256

Simple Exponential Smoothing 260

Seasonality with Additive Effects 263

Seasonality with Multiplicative Effects 268

Conclusion 272

CHAPTER 16 Case Study 16—Determining Lost Sales Using Nonregression Trend Models 273

When Averaging Techniques Are Not Appropriate 273

Double Moving Average 275

Double Exponential Smoothing (Holt’s Method) 277

Triple Exponential Smoothing (Holt-Winter’s Method) for Additive Seasonal Effects 279

Triple Exponential Smoothing (Holt-Winter’s Method) for Multiplicative Seasonal Effects 285

Conclusion 288

APPENDIX The Next Frontier in the Application of Statistics 291

The Technology 291

EViews 291

Minitab 292

NCSS 292

The R Project for Statistical Computing 293

SAS 294

SPSS 295

Stata 296

WINKS SDA 7 Professional 298

Conclusion 299

Bibliography of Suggested Statistics Textbooks 301

Glossary of Statistical Terms 303

About the Authors 317

Index 319