A Quantitative Approach to Commercial Damages E-Book

Mark G. Filler

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 386

Veröffentlichungsjahr: 2012

Beschreibung

How-to guidance for measuring lost profits due to business interruption damages A Quantitative Approach to Commercial Damages explains the complicated process of measuring business interruption damages, whether they are losses are from natural or man-made disasters, or whether the performance of one company adversely affects the performance of another. Using a methodology built around case studies integrated with solution tools, this book is presented step by step from the analysis damages perspective to aid in preparing a damage claim. Over 250 screen shots are included and key cell formulas that show how to construct a formula and lay it out on the spreadsheet. * Includes Excel spreadsheet applications and key cell formulas for those who wish to construct their own spreadsheets * Offers a step-by-step approach to computing damages using case studies and over 250 screen shots Often in the course of business, a firm will be damaged by the actions of another individual or company, such as a fire that shuts down a restaurant for two months. Often, this results in the filing of a business interruption claim. Discover how to measure business losses with the proven guidance found in A Quantitative Approach to Commercial Damages.

Leseprobe

Contents

Cover

Series

Title Page

Copyright

Dedication

Preface

Is This a Course in Statistics?

How This Book Is Set Up

The Job of the Testifying Expert

About the Companion Web Site—Spreadsheet Availability

Acknowledgments

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

The Three Big Statistical Ideas

Introduction to the Idea of Lost Profits

Choosing a Forecasting Model

Conventional Forecasting Models

Other Applications of Statistical Models

Conclusion

Notes

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

The Steps of Data Analysis

Conclusion

Notes

CHAPTER 2: Case Study 2—Trend and Seasonality Analysis

Claim Submitted

Claim Review

Occupancy Percentages

Trend, Seasonality, and Noise

Trendline Test

Cycle Testing

Conclusion

Note

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

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

A Brief Introduction to Simple Linear Regression

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

Regression Statistics

Tests and Analysis of Residuals

Testing the Linearity Assumption

Testing the Normality Assumption

Testing the Constant Variance Assumption

Testing the Independence Assumption

Testing the No Errors-in-Variables Assumption

Testing the No Multicollinearity Assumption

Conclusion

Note

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

Correlation with Industry Sales

Conversion to Quarterly Data

Quadratic Regression Model

Problems with the Quarterly Quadratic Model

Substituting a Monthly Quadratic Model

Conclusion

Note

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

Exploratory Data Analysis

Seasonal Indexes versus Dummy Variables

Creation of the Optimized Seasonal Indexes

Creation of the Monthly Time Series Model

Creation of the Composite Model

Conclusion

Notes

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

Outline of the Case

Testing for Noise in the Data

Converting to Quarterly Data

Optimizing Seasonal Indexes

Exogenous Predictor Variable

Interrupted Time Series Analysis

“But For” Sales Forecast

Transforming the Dependent Variable

Dealing with Mitigation

Computing Saved Costs and Expenses

Conclusion

Note

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

Preliminary Tests of the Data

Selecting the Appropriate Regression Model

Finding the Facts Behind the Figures

Conclusion

Notes

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

Graph Your Data

Industry Comparisons

Accounting for Seasonality

Accounting for Trend

Accounting for Interventions

Forecasting “Should Be” Sales

Testing the Model

Final Sales Forecast

Conclusion

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

Classifying Cost Behavior

An Arbitrary Classification

Graph Your Data

Testing the Assumption of Significance

Expense Drivers

Conclusion

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

Graph Your Data

Regression Summary Output of the First Model

Search for Other Independent Variables

Regression Summary Output of the Second Model

Conclusion

CHAPTER 11: Case Study 11—Analysis of and Modification to Opposing Experts' Reports

Background Information

Stipulated Facts and Data

The Flaw Common to Both Experts

Defendant's Expert's Report

Plaintiff's Expert's Report

The Modified-Exponential Growth Curve

Four Damages Models

Conclusion

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

A Review of Methods of Loss Calculation

A Case Study: Dunlap Drive-In Diner

Skeptical Analysis Using the Fraud Theory Approach

Discussion

Conclusion

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

Month Length Adjustment

Graph Your Data

Worksheet Setup

Selection of Length of Prior Period

Reasonableness Test

Conclusion

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

Need for Analytical Tests

Graph Your Data

Statistical Procedures

Tests for Randomness

Tests for Trend and Seasonality

Testing for Seasonality and Trend with a Regression Model

Conclusion

Notes

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

Prediction Errors and Their Measurement

Moving Averages

Array Formulas

Weighted Moving Averages

Simple Exponential Smoothing

Seasonality with Additive Effects

Seasonality with Multiplicative Effects

Conclusion

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

When Averaging Techniques Are Not Appropriate

Double Moving Average

Double Exponential Smoothing (Holt's Method)

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

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

Conclusion

APPENDIX: The Next Frontier in the Application of Statistics

The Technology

Conclusion

Bibliography of Suggested Statistics Textbooks

Glossary of Statistical Terms

About the Authors

Index

The National Association of Certified Valuators and Analysts (NACVA) supports the users of business and intangible asset valuation services and financial forensic services, including damages determinations of all kinds and fraud detection and prevention, by training and certifying financial professionals in these disciplines. NACVA training includes Continuing Professional Education (CPE) credit and is available to both members and non-members. Contact NACVA at [phone] or visit the web site at www.NACVA.com.

Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Filler, Mark, 1942–

A quantitative approach to commercial damages : applying statistics to the measurement of lost profits / Mark Filler, James DiGabriele.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-118-07259-2 (cloth/website); ISBN 978-1-118-22244-7 (ebk);

ISBN 978-1-118-23637-6 (ebk); ISBN 978-1-118-26104-0 (ebk)

1. Lost profits damages–Valuation–Statistical methods. I. DiGabriele,

James A., 1962–II. Title.

K837.F55 2012

347′.077–dc23

2011050886

To my children, Joshua David and Rachel Leah, who have exceeded my hopes and expectations.

—MGF

To my wife Lori, my sons, Daniel, James, and John. I thank them for their encouragement, love, support, and patience during this journey.

—JAD

Preface

From years of presenting at conferences and seminars, participating in roundtable discussions and case study analyses, and mentoring fellow practitioners, it became obvious to us that the typical ABV, CBA, ASA, or CVA who was attempting to calculate economic damages either as a stream of lost profits or as lost value of the business using the direct market data method had little knowledge of either statistical methods or the advantages to be obtained by applying them to the task at hand.

This book is intended for practitioners who have some experience in the field of calculating economic damages and who are looking to acquire some new tools for their toolkit—tools that are more sophisticated and flexible than simple averaging techniques. These typical practitioners will remember little from their college statistics course and will not have access to or be capable of using stand-alone statistical packages such as SAS, SPSS, Stata, and so on. But they will be familiar with Excel, and our pedagogical approach is to demonstrate the use of the statistical tools that come either built into Excel or as add-ins that are freely or inexpensively available.

The level of knowledge that is required to get the maximum benefit from this book does not exceed that needed for an introductory statistics course. Therefore, this book is not designed for trained statisticians or PhDs in economics or finance whose education, knowledge, and training far exceed the fundamentals expounded herein.

Is This a Course in Statistics?

The simple answer is no! This book is intended to be an introduction and a “how-to” of some basic statistical techniques that can be useful in a lost profits analysis.  It is not, however, meant to replace a statistical text or give the reader an in-depth understanding of statistics. 

We have provided a glossary of terms as they are defined by standard statistical textbooks, and a bibliography that provides the reader with sources to study for a more in-depth analysis of the concepts introduced in this book. 

While the book focuses on the basic statistical applications as found in Excel or its add-ins, readers are encouraged to undertake a more thorough understanding of the conceptual underpinnings of the techniques by referring to the textbooks recommended in the bibliography.

At a minimum, we suggest the following three Excel add-ins. First, there is the StatPlus add-in that comes with Berk and Carey's book, Data Analysis with Microsoft Excel. Second, there is the popular free downloadable add-in, Essential Regression. And last, if you can find it on the Internet, Gerry LaBute's downloadable add-in, Gerry's Stats Tools. The latter two add-ins come with handbooks that not only serve as instruction manuals for the software, but are primers for regression and statistics in general, respectively.

How This Book Is Set Up

The organizing principle that motivates this book is the attempt to match up Excel's and its add-ins' statistical tools with common, quotidian problems and issues that damages analysts face in their day-to-day practices. We approached the subject matter from both sides of the matchup.

First, we examined the statistical tools available in Excel's Analysis ToolPak, its statistical formulas, and the specialized tools available in the add-ins and asked ourselves: In what ways can we apply any of these tools to commercial damages cases? Second, we reviewed the literature looking for typical commercial damages cases and asked: Is there a statistical solution to this problem? The results of our back and forth approach are the 16 case studies in this book, with each (as the Contents listing shows at the front of this book) presented as its own chapter.

Case Study 1 demonstrates how to use the standard deviation to determine if some number, say, a period's gross margin or a month's sales, falls within an expected range based on past performance.

Case Study 2 concerns itself with testing the sales history of the XYZ Motel to determine if there is an upward trend in the data as asserted by the claimant.

Case Study 3 is an introduction to regression analysis in the context of measuring damages for lost profits as the value of a business destroyed by the actions of the defendant.

Case Study 4 returns to the XYZ Motel and the forecasting of expected sales during the period of restoration using an econometric regression model.

Case Study 5 uses the XYZ Motel data once again to forecast expected sales during the period of restoration using a time series regression model.

Case Study 6 demonstrates the forecasting of sales using an econometric regression model, the determination of saved expenses using a simple linear regression model, and introduces the idea of interrupted time series analysis.

Case Study 7 involves the comparison of pre- and postincident sales and demonstrates techniques to answer the question: Did sales really fall off after the incident?

Case Study 8 demonstrates the forecasting of sales using a time series regression model and tests the significance of an intervening event with the use of interrupted time series analysis.

Case Study 9 involves the issue of cost behavior and estimation.

Case Study 10 presents a problem concerning the determination of saved expenses and introduces the issue of statistical significance vs. practical significance.

Case Study 11 presents the plaintiff's and the defendant's expert's reports in a breach of contract action, points out the flaws in each, and offers a reconciling resolution to their differences.

Case Study 12 is about the application of forensic accounting principles to a lost profits case.

Case Study 13 shows how to set up and use a nonstatistical method for accounting for trend and seasonality when forecasting expected sales.

Case Study 14 involves techniques used to analyze historical sales data searching for trend and seasonality.

Case Study 15 displays nonregression techniques for forecasting sales when the historical sales data is stationary.

Case Study 16 displays nonregression techniques for forecasting sales when the historical sales data is nonstationary.

The Job of the Testifying Expert1

According to Federal Rule of Evidence 702, an expert will be allowed to testify in the form of an opinion if,

1. The testimony is based upon sufficient facts or data.

2. The testimony is the product of reliable principles and methods.

3. The witness has applied the principles and methods reliably to the facts of the case.

In addition, the opinion given must be “within a high degree of (economic or financial) certainty.” In other words, a trier of fact, either a judge or jury, is looking for an opinion that will help them to “understand the evidence or to determine a fact in issue.” An academic treatise that increases the storehouse of knowledge might meet that requirement, but given the amount, accuracy, and verifiability of the facts and data available to the expert in a litigation matter, will generally not be forthcoming. Therefore, given the different purposes of the researcher and the testifying expert, different methods of analysis and different uses of the traditional research tools is to be expected.

In the course of this book we will be demonstrating selected statistical techniques to be applied in lost profits cases, where the end result is to form an opinion as to the amount of economic damages, even if there are limits to the facts and data and all the supporting documentation you want is not available. The testifying expert, while using research tools familiar to academics, is attempting to assist the trier of fact, and therefore is not engaged in an “exhaustive search for cosmic understanding but for the particularized resolution of legal disputes.”

About the Companion Web Site—Spreadsheet Availability

There is a companion web site to this book—found at www.wiley.com/go/commercialdamages—that contains all the spreadsheets for the case studies in this book. So, you have a choice—you can create the spreadsheets from scratch, following the instructions contained in each chapter, or you can simply download them from the web site and start your analysis immediately. For pedagogical purposes, we recommend that you create your own spreadsheets—there's something about putting them together yourself that leads to a quicker understanding of their purpose.

1. Adapted from the paper “To Infinity and Beyond: Statistical Techniques Appraising the Closely Held Business,” presented by Drs. Tom Stanton and Joe Vinso at the 20th Annual IBA Conference, San Antonio, TX, January 1998.

Acknowledgments

The authors wish to express their gratitude and appreciation to the following individuals who served as readers and reviewers of this book.

David H. Goodman, MBA, CPA/ABV, CVA

J. Richard Claywell, CPA/ABV, ASA, CBA, CVA, CM&AA, CFFA, CFD, ABAR

John E. Barrett, Jr., CPA/ABV, CBA, CVA

James F. McNulty, CPA

We would also like to thank Nancy J. Fannon, CPA/ABV, ASA, MCBA, for first suggesting the idea of this book and for initially reviewing the introduction and the first six chapters.

INTRODUCTION

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

To get the most out of the case studies in this book, the reader needs to attain a minimum amount of statistical knowledge.

The Three Big Statistical Ideas

There are Three Big Statistical Ideas: variation, correlation, and rejection region (or area). If we can build sufficient intuition about these interrelated concepts, then we can construct a raft for ourselves upon which we can explore the bayou of statistical analysis for lost profits. Therefore, what follows is a very broad introduction to statistics, which does not allow us to explain or define every technical term that appears. To assist you, we have included all those technical terms in a Glossary at the end of the book where they are defined or explained.