The Layman s Use of Regression Analysis for Business Valuation

The Layman s Use of Regression Analysis for Business Valuation By Ronald D. Rudich, CPA/ABV/CFF, MS CVA, CBA/BVAL/ABAR, CM&AA, CMEA, SBA rrudich@gsg-cpa.com D: 410.517.6838 F: 410.517.6738 C: 410.812.1230 MACPA 2013 Business Valuation Conference Hilton Baltimore BWI Airport, Linthicum May 10, 2013 Ronald D. Rudich, CPA/ABV/CFF, MST, CBA/ABAR/BVAL, CVA, CM&AA, CMEA Owings Mills, MD D: (410) 517-6838 C: (410) 812-1230 F: (410) 517-6738 E: rrudich@gsg-cpa.com Ron is the Senior Director of Business Valuation and Litigation Support Services for Gorfine, Schiller & Gardyn, P.A., a 90 member Baltimore area CPA and business consulting firm. His responsibilities include valuations of closely held and publicly traded companies, machinery and equipment appraisals, strategic business planning, budget and forecasting services, business consulting, business loss computations, depositions, and court testimony. He has written articles and lectures, mentors, and teaches business valuation. Mr. Rudich has written two white papers; (1) Valuing the Difference Between Voting and Non Voting Shares of Stock, published in Business Valuation Update, November 2010 by Business Valuation Resources, LLC, and (2) Analyzing the IBA Database Transactions Results, published in Business Appraisal Practice, Winter 2006/2007 by the Institute of Business Appraisers, Inc. For the Institute of Business Appraisers, he was elected as Chair of the Board of Governors for a two year term in June 2012 and appointed to the Board for a three year term in June 2011, appointed as Chair of the Accredited in Business Appraisal Review (ABAR) Appeals Task Force that provides technical guidance and support on ABAR reviews as of January 2011, and is a report reviewer for the Quality Review Committee (QRC) for those seeking a credential certification from 2008 to the present. Mr. Rudich was selected into the Founders Circle of the of the Alliance of Merger & Acquisition Advisors in January 2013, elected to the Advisory Board in 2004, and received the 2008 Chair of the Year award in January 2009. He was admitted to the Westlaw Round Table Group, Washington, DC expert network as a Round Table Scholar in January 2009 and recognized by SmartCEO as one of the Top CPAs in the Baltimore/Washington, DC area in their September 2008 issue. 2 1

LEARNING OBJECTIVES What is regression analysis and how will it assist you in determining the indicated equity value? Understanding what are the dependent and independent variables and their interrelationship. How to regress your database results utilizing Excel. How to graph the metric results. 3 LEARNING OBJECTIVES Understanding the regression formula and how to use the slope and intercept to determine an indicated value. Understanding the nuances of how BIZCOMPS, the IBA Database and Pratt s Stats measure their data that require a recompilation by a valuator. Using the R Square to determine the weighting for the indicated value instead of a subjective assumption by the valuator. 4 2

DEFINITION OF REGRESSION The act of going back to a previous place or state; return or reversion. Retrogradation; Retrogression. Reversion to an earlier or less advanced state or form or to a common or general type (Biology). 5 DEFINITION OF REGRESSION The reversion to a chronologically earlier or less adapted pattern of behavior and feeling (Psychoanalysis). The adoption by an adult or adolescent of behavior more appropriate to a child, especially as a defense mechanism to avoid anxiety. 6 3

OUR DEFINITION OF REGRESSION STATISTICS a. The analysis or measure of the association between one variable (the dependent variable Y ) and one or more other variables (the independent variables X ), usually formulated in an equation in which the independent variables have parametric coefficients, which may enable future values of the dependent variable to be predicted. 7 The Regression Equation of a Line Y = mx + b Where Y = the Slope * X (+ or ) the Y-Intercept * Remember it this way!!! Y is Dependent (the resultant answer) on X s independently selected specific parameter (Factor of Choice). * The IBA Market Data found at www.vswebapp.com and BIZCOMPS data found at www.keyvaluedata.com provide this equation within its charts. 8 4

What Are Dependent Variables? The Y Factor in the equation is: PRICE; SALES PRICE MVIC (market value of invested capital)* * This metric is found when using Business Valuation Resources Pratt s Stats and Pratt s Public Stats (www.bvmarketdata.com) 9 What Are Independent Variables? The X Factor in the equation SALES (revenues) SDEs (discretionary earnings) EBIT EBITDA 10 5

Why Regression is Important in Valuation to Mitigate RISK!!! Without regression analysis, you will not be able to provide support or conclusive evidence for the selected metric. You will be able to demonstrate that, by utilizing the selected data inclusive of outliers, it provides cogent results that proves you did not cherry-pick your results. 11 Regression simply trends the relationship results (i.e.; sales price to gross sales or sales price to seller s discretionary earnings) of the known ratios to establish a variance to a trendline. A trendline is the line which intersects the results approximating the most centrist straight line. Think of a graph that has a line going through the middle of the results. Each ratio results in a point that is a specific distance from the trendline; the closer the result is to the trendline the more reliable the data becomes. 12 6

IN A PERFECT CORRELATION, ALL POINTS WOULD RESIDE ON THE TRENDLINE!!! 13 This regression technique is known as R- squared or the coefficient of determination. The R-square yields a measure of the result from zero to one (0.0 1.0). An R-squared result that is closer to zero demonstrates a lack of reliability while an R-squared result that is closer to one (1.0) demonstrates high reliability. Therefore, an R-squared result that is greater than 0.500 for all of the data graphed is more reliable than an R- squared that is below 0.500. 14 7

Why is Regression Important in Valuation? It provides conclusive evidence that a series of dependent and independent associated quantifiers provide individual metrics (results) that are (for the most part) relatively either similar or dissimilar to each other. It will appear as either Highly correlated or Not correlated!! 15 What Does Regression Analysis Tell the Valuator? How well correlated the sales price (the dependent variable) is to the independent value variable (Sales, EBIT, etc.) IN OTHER WORDS How much does the sales price depend on each one of the chosen metrics. If well correlated, then completed transaction methodology is meaningful. 16 8

What Does Regression Analysis Tell the Valuator? OR PUT ANOTHER WAY How well does the level of revenue, for example, predict what a business in that industry would sell for OR, How likely is it that the sales price of a business in a particular industry is determined as it relates to the revenue, EBIT, EBITDA, GP, SDE, etc. 17 Illustration Sample Data: * X Y X Y Sales Price Sales Price (000s) (000s) Metric (000s) (000s) Metric 1,000.1 482.0 0.482 777.3 395.0 0.508 968.7 455.5 0.470 1,582.4 800.0 0.506 455.3 301.1 0.661 1,181.4 600.0 0.508 1,208.7 600.0 0.496 1,822.6 950.0 0.521 555.9 300.0 0.540 788.2 450.0 0.571 688.8 350.8 0.509 878.8 500.0 0.569 3,201.4 1,800.0 0.562 901.6 650.0 0.721 * Insert into Excel using a column for each X and Y statistic 18 9

Easily Identified Metrics The: High 0.721 Low 0.470 Mean 0.545 (Average) Median 0.515 (Mid-Point) 19 Regression Using Excel * Open Tools, then Go down to Data Analysis, then Scroll down to Regression * If you don t see Data Analysis, go to Tools/Add-Ins, select Analysis ToolPak and click OK. This will download and install the ToolPak. From then on it should be in your Tools drop down menu. 20 10

Regression Using Excel The box will look like this: 21 First, click your cursor in the Input Y Range box and select the dependent data cells inclusive of the title (Price) and then repeat by clicking your cursor in the Input X Range box for the independent data inclusive of the title (Sales): * * You must make sure that: 1) There are no blank lines 2) No non-numeric data (except for the title) 3) If you have blanks, alpha data, such as N/A or None eliminate both the independent and dependent variables by highlighting both, right click, select Delete and Shift Cells Up and click OK. 22 11

Then click the box marked Labels. Then click the radio button marked Output Range. Move your cursor to the box adjacent to the radio button and select a cell in the workbook where you want the Excel Regression Summary Output to appear. 23 When completed the Regression Input box should look like this; then press OK : 24 12

Your result will look like this: This is the Regression Metric: This is the (+ or -) Y-Intercept Metric This is the Slope Metric 25 Preliminarily the Summary Output Provides a Value Indication Therefore, using the formula to determine the value indication is as follows: Y = slope*x [the independent variable] + Y-Intercept, where X is the company s sales (Assume $4,865,800) for the current year. 26 13

Then: Y=0.54639138 * $4,865,800 + (-8,141.55.) is: Y=$2,658,631 8,142** [**WHY?..because if the source amounts are truncated (as listed in thousandths of dollars in the IBA and Bizcomps data) then the answer must be expanded by three (3) decimal places] Therefore the indicated value of the company s equity is: $ 2,650,489 27 Charting the X, Y Metrics Click on the Chart Wizard on the Tool Bar Select the XY (Scatter) chart type Select the default (upper left) Chart Sub- Type Click Next> 28 14

Charting the X, Y Metrics The Chart Wizard will look like this ---> 29 Charting the X, Y Metrics From the X, Y graph (as seen on page 22) highlight only the data NOT the words or letters!! You should notice that a specific range has been noted with a graph in Column format ------------ Click the Next> button. 30 15

Charting the X, Y Metrics The next Chart Wizard Step will look like ---- Then: Enter Your Chart Title Enter the names of the X and Y axes Click the Finish> button. 31 Charting the X, Y Metrics The Chart Wizard should look like ---- 32 16

The Resultant Chart should look like this ----- Charting the X, Y Metrics 33 Charting the X, Y Metrics NOTE: When you left click on the graph, six black squares appear on edges of the graph that will permit you to move and size the graph AND the word DATA on the tool bar changes to the word CHART. This will permit you to add a TRENDLINE to your chart. Click on the word Chart on the toolbar and select ADD TRENDLINE. Choose the default Name Trend/Regression Type in the upper left and click OK and Excel will automatically place the trendline in the most centrist part through the graphed data points. 34 17

Charting the X, Y Metrics Your Graph should look like this ----- 35 Charting the X, Y Metrics In order to change the R2 to R 2 (to property reflect R-squared) you must left click on the graph and touch the title with your mouse and click once. The entire title will then be boxed. Hold down the left click on the mouse and highlight the 2 only and right click on the highlighted 2 and chose Format Chart Title. This is what you should see Select the Superscript box and click OK. 36 18

Charting the X, Y Metrics Your graph will now appear as follows: 37 Now, Back to the Indicated Value We previously equated an indicated value of $ 2,650,489 on sales of $4,865,000 using the slope and intercept formula. Now based on the median metric (0.515) we may determine another indicated equity value. That being $2,505,475 ($4,865,000*0.515). 38 19

Which Indicated Value is Correct? If the company you are valuing demonstrates a superior or inferior comparison to industry metrics, you may want to stratify the transaction results in order to determine what metric (other than the median) should be utilized. 39 Stratifying the Transaction Results Stratifying the data depends on how many transactions there are in your sample. There should be at least six (6) transactions in each segment. 40 20

Stratifying the Transaction Results Raymond C. Miles, CBA, ASA stated* in part that, At least 5 transactions are needed in order to gain a usable estimate of the market average price to revenue (P/G) or price to earnings (P/E) ratio. This need for at least 5 comparable transactions applies to all methods under the Market Approach, not just to the Direct Market Data Method. With fewer than 5 transactions, the appraiser s understanding of the market is not adequate to use as a basis for estimating the market value of the subject business. How To Use The IBA Market Data Base, Part XXXV, About The IBA Transaction Database, Copyright 2003 41 Raymond C. Miles Continues With more than 5 but less than twenty transactions, the best that can be done is to divide the market into two parts, (a) P/G or P/E ratio above average, and (b) P/G or P/E ratio below average. With at least 20 transactions, the market can be divided into four parts, upper 25% of P/G or P/E ratios, second highest 25% of P/G or P/E ratios, etc. This greatly facilitates placing the subject business in the appropriate portion of the market. Similarly, with 50 or more transactions, the market can be divided in deciles, and so on with more than 50 transactions. 42 21

Stratifying the Transaction Results Since we only have fourteen (14) transactions in our sample, we will divide them into two (2) segments. 43 Stratifying the Transaction Metrics From High to Low Sales Price P/S Sales Price P/S (000s) (000s) Metric (000s) (000s) Metric 901.6 650.0 0.721 688.8 350.8 0.509 455.3 301.1 0.661 1,181.4 600.0 0.508 788.2 450.1 0.571 777.3 395.0 0.508 878.8 500.0 0.569 1,582.4 800.0 0.506 3,201.4 1,800.0 0.562 1,208.7 600.0 0.496 555.9 300.0 0.540 1,000.1 482.0 0.482 1,822.6 950.0 0.521 968.7 455.5 0.470 High 0.721 High 0.509 Low 0.521 Low 0.470 Mean 0.592 Mean 0.497 Median 0.569 Median 0.506 44 22

Indicated Value From Stratification Sales $ 4,865,000 Median P/S metric from the upper half; assuming a company superior to the industry 0.569 Indicated Equity Value $ 2,768,185 45 Comparison of Indicated Equity Values Median of all Results $ 2,505,475 Regression Formula Result (from the Slope Intercept calculation) $ 2,650,489 Median of Upper Half Results $ 2,768,185 46 23

Which Value is CORRECT??!! The Answer Is It s Up To You!!! This is an ART not a Science. You may select any individual result, the average or the median. 47 BUT, Are They the Equity Values??? Remember If your transactions were selected from the IBA or BIZCOMPS databases, they represent ASSET transactions and require adjustments to affect an equity value. 48 24

Conversion From Asset Sales to Equity Values BIZCOMPS DATABASE: All transactions in the BIZCOMPS database were either asset sales or were converted to an asset sale, meaning that the only assets that were sold were Fixtures & Equipment ( F&Eq ) and Goodwill. To convert this value to an equity interest of an owner or seller of a business requires a couple of steps. First, add all short and long-term assets to the value, less the value of the F&Eq. The F&Eq employed in the business have already been included in the various transactions. The second step is to subtract all liabilities (the business is considered to be debt-free at the time of sale). 49 Conversion From Asset Sales to Equity Values BIZCOMPS Bizcomps Indicated Asset Value + Current assets + Long-term assets w/o Fixed assets (-) All Liabilities = Indicated Equity Value 50 25

Conversion From Asset Sales to Equity Values THE IBA DATABASE*: All transactions listed in the IBA Market Data Base are asset sales rather than sales of capital stock. The content of the transactions in the database reflects what is customarily included in sales of the specific kind of business. Although this may differ somewhat from one kind of business to another, a survey conducted by IBA confirms that, for most kinds of businesses, the selling price listed includes inventory, fixed assets, leaseholds, and intangibles 51 Conversion From Asset Sales to Equity Values such as goodwill, but that sales do not include accounts receivable, or liabilities other than those related to financing of any of the fixed assets. Inventory included in the sale is usually priced at closing, and is included in the total price as reported in the database. Liabilities are reflected in the reported sale price if they relate to assets that are included in the sale. Thus notes payable secured by fixed assets will be reflected in the sale price. * How To Use The IBA Market Data Base, Part XXVI, by Raymond C. Miles, CBA, ASA, Copyright 1999 as published in the Technical Studies of the IBA Transaction Database 52 26

Conversion From Asset Sales to Equity Values - IBA Indicated Asset Value + Cash, Accounts Receivable (No Inventory) + In some cases Real Estate + Other Assets (Deposits, Prepaid, etc.) (-) Non-related to fixed assets Liabilities (-) Other Payables = Indicated Equity Value 53 Furthermore, re: IBA & BIZCOMPS Data If you are using the Sellers Discretionary Earnings (SDE or DE) each database addresses this metric differently. BIZCOMPS DATABASE : SDE is calculated by adding to Net Income before taxes: Amortization, Depreciation, Interest, Owner s compensation, Owner s benefits, Non-business related expenses, and onetime-only expenses. 54 27

Furthermore, re: IBA & BIZCOMPS Data THE IBA DATABASE: Annual Earnings ( Ann. Earn. ) is reported annual earnings before owner s compensation, interest and taxes. NOTE: BIZCOMPS does NOT subtract interest income, and IBA does NOT add back depreciation, amortization, owner s benefits, non-business related expenses, and onetime-only expenses or subtract interest income. 55 SDE for BIZCOMPS & IBA BIZCOMPS: Operating Profit before Taxes Add: Owner s Comp. (1 owner) Owner s Benefits (P/r taxes, Pension*) Amortization & Depreciation Interest expense Non-Business expense One-time Extraordinary expenses Less: Interest income IBA: Earnings Before owner s Compensation, Interest, Taxes Add: Amortization Depreciation Non-Business expense Extraordinary expenses Owner s Benefits (P/r taxes, Health ins., Pension, etc.*) Less: Interest income 56 28

Business Valuation Resources Database Pratt s Stats provides results related to Private Transactions. Pratt s Public stats provides results related to Publicly traded transactions. 57 Business Valuation Resources Database Both databases provide the following major data points*: Statistical Mean Harmonic Mean Statistical Median Income Data Asset Data Date of Sale Coefficient of Variation Market Value of Invested Capital ( MVIC ) * All information re: Pratt databases are printed with permission from Business Valuation Resources by Lucretia Lyons, President 58 29

Business Valuation Resources Database Noncompete Value Asset or Stock sale Valuation Multiples Profitability Ratios Leverage Ratios Specific EBITDA Liquidity Ratios Activity Ratios Company Type (C corp., S corp., LLC, etc.) Specific Transaction information, and Discretionary Earnings 59 Understanding A Valuation Statistic Understanding the Coefficient of Variation Definition of the CV : The coefficient of variation is defined as the ratio of the standard deviation to the mean. 60 30

Understanding A Valuation Statistic Advantages of the CV: The CV is useful because the standard deviation of data must always be understood in the context of the mean of the data. Instead, the actual value of the CV is independent of the unit in which the measurement has been taken, so it is a dimensionless number. For comparison between data sets with different units or widely different means, one should use the CV instead of the standard deviation. 61 Understanding A Valuation Statistic Disadvantages of the CV: When the mean value is close to zero, the CV will approach infinity and is therefore sensitive to small changes in the mean. This is often the case if the values do not originate from a ratio scale. Unlike the standard deviation, it cannot be used directly to construct confidence intervals for the mean. 62 31

Understanding A Valuation Statistic The CV may provide you with a false sense of confidence that the mean or median result is a reliable metric. Therefore, you must prepare regression analyses on your data points. You cannot rely on a low CV number to ensure that you have reliable data. 63 Business Valuation Resources Database It is extremely important to segregate the Asset sale data from the Stock sale data. Do not commingle these results. Asset Sale Data must be converted to equity (Stock) data much the same as you would change the Bizcomps or IBA database results. 64 32

Business Valuation Resources Database Note: BVR includes the Employment Agreement Value and the Noncompete Value in the Market Value of Invested Capital ( MVIC ). I remove these values and restate MVIC before I calculate the MVIC/Sales, MVIC/GP, etc. metrics. 65 Business Valuation Resources Database When using the most reliable metric MVIC (to the statistic of your choosing; net sales, EBIT, EBITDA), do not forget to subtract the long-term interest bearing debt to attain the equity value of the enterprise. 66 33

Using Regression For Analytical Weighting! Suppose the you have results as follows; all converted to an Indicated Equity Value: R 2 IBA; Price to Sales $2,676,531 0.5994 Bizcomps; Price to Sales 2,588,829 0.6788 Pratt; MVIC to Sales 2,899,802 0.8344 Which value do you choose? Or, do you add them and divide by 3 to yield and average? Or, do you just go with the median? 67 Using Regression For Analytical Weighting! To remove the subjectivity from your chosen indicated value, let your regression analyses assist in providing the regression weighted indicated value. Indicated Amount R 2 Weight % Amount*Wgt. $ 2,676,531 0.5994 28.37 $ 759,332 2,588,829 0.6788 32.13 831,791 2,899,802 0.8344 39.50 1,145,422 Totals 2.1126 100.00 $ 2,736,544 68 34

Using Regression For Weighting! Therefore, your Indicated Fair Market Value of the Equity Rounded is.. $ 2,737,000 And, your personal subjective decision is removed from the process. 69 REMEMBER By Using Regression Analysis properly will enable you to become a more.. Credible Professional Appraiser 70 35

Thank You Very Much For Your Participation 71 36