Size premium in small business valuation: Analysis of closely-held firms

Galbraith, Craig S. Article Size premium in small business valuation: Analysis of closely-held firms The Journal of Entrepreneurial Finance (JEF) Provided in Cooperation with: The Academy of Entrepreneurial Finance (AEF), Los Angeles, CA, USA Suggested Citation: Galbraith, Craig S. (2025) : Size premium in small business valuation: Analysis of closely-held firms, The Journal of Entrepreneurial Finance (JEF), ISSN 2373-1761, Pepperdine University, Graziadio School of Business and Management and The Academy of Entrepreneurial Finance (AEF), Malibu, CA and Los Angeles, CA, Vol. 27, Iss. 1, pp. 31-46, https://doi.org/10.57229/2373-1761.1498 This Version is available at: https://hdl.handle.net/10419/319786 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ The Journal of Entrepreneurial Finance The Journal of Entrepreneurial Finance Volume 27 Issue 1 2025 Article 2 2025 SIZE PREMIUM IN SMALL BUSINESS VALUATION: ANALYSIS OF SIZE PREMIUM IN SMALL BUSINESS VALUATION: ANALYSIS OF CLOSELY-HELD FIRMS CLOSELY-HELD FIRMS Craig S. Galbraith University of North Carolina - Wilmington Follow this and additional works at: https://digitalcommons.pepperdine.edu/jef Part of the Entrepreneurial and Small Business Operations Commons Recommended Citation Recommended Citation Galbraith, Craig S. (2025) "SIZE PREMIUM IN SMALL BUSINESS VALUATION: ANALYSIS OF CLOSELYHELD FIRMS," The Journal of Entrepreneurial Finance : Vol. 27: Iss. 1, pp. 31-46. DOI: https://doi.org/10.57229/2373-1761.1498 Available at: https://digitalcommons.pepperdine.edu/jef/vol27/iss1/2 This Article is brought to you for free and open access by the Graziadio School of Business and Management at Pepperdine Digital Commons. It has been accepted for inclusion in The Journal of Entrepreneurial Finance by an authorized editor of Pepperdine Digital Commons. For more information, please contact bailey[email protected]. Size Premiums in Small Business Valuation: Analysis of Closely-Held Firms Craig S. Galbraith Duke Progress Entergy/Betty Cameron Distinguished Professor University of North Carolina Wilmington, Wilmington, NC USA [email protected] ABSTRACT Abstract : One of the most misunderstood components of valuing a small closely-held business is how to address the impact of small size. Most closely-held enterprises are relatively small in size, with market values less than $1million. Many small mom and pop operations, or single owner-operator family businesses, often have market values even smaller. The most common method to account for size is to use the size premium reports from Kroll or another financial data service provider. However, these small firm premiums are determined exclusively from publicly-traded firms, where even the category of the smallest publicly-traded firms are still magnitudes larger than the typical small closelyheld firm. This study examines the Kroll size premium data on publicly-traded firms and compares it with an analysis of size data from a proprietary database of closely-held firm transactions. We develop various models that better assess the impact of size on the cost of equity calculations for small, closelyheld firms. Key Words: Size premium; Valuation; Closely-held firms; Discount rates, Capitalization rates 1. Introduction The valuation of small closely-held companies, most of which are single owner-operator or entrepreneurial entities, always presents a difficult estimation process. There are a variety of issues the business valuator of a small business needs to consider, such as accuracy of financial statements, adjusting for fair market expenses, and the nature of owner compensation. There are three broad categories of methods used to value small closely-held firms: asset methods, market comparable methods, and income methods. In general, the asset method calculates the minimum value of a business (approximation of net liquidation), while the comparable and income methods represent “going concern” values. The comparable methods inevitably attempt to employ transactions of similar firms and then apply various metrics such as revenue or gross profit multiples to the target firm. Income methods, on the other hand, examine the earnings of the firm. The most common income-based valuation method used in practice is the capitalization of earnings (or free cashflows/FCFE) methods. This involves applying a capitalization rate to the adjusted earnings in order to obtain a fair market equity value of the target firm. The calculation of the appropriate capitalization rate requires an estimate of the associated discount rate, which is then adjusted for growth. In fact, the capitalization of earnings method is essentially an approximation of the present value of future earnings or cashflows under the assumption that past earnings will continue into the future at a somewhat constant growth rate. For this reason, capitalization of earnings methods should be applied to relatively stable firms. It is generally not appropriate for early-stage technology firms, intellectual property valuations, or situations where the future financial situation might be very different from the past – in these cases a 31 Galbraith: Size Premium in Small Business ValuationPublished by Pepperdine Digital Commons, 2025 discounted future cashflow analysis is generally used. However, in many cases of small closely-held firms, with stable past earnings, and no major expected changes in the competitive environment in the future, the capitalization of earnings, with its underlying theoretical assumption of discounted cashflows, is a reasonable and often-used method. While income-based valuation methods have their own set of constraints, such as developing accurate earnings or cashflow forecasts for the firm, a particular requirement for calculating discounted earnings, or its associated capitalization of earnings, is the development of an appropriate discount rate, or cost of equity. Unlike the cost of debt, which can be determined from a weighted average of interest rates, the cost of equity requires significant thought and analysis. While there are many different approaches associated with this calculation, the most common way of calculating the cost of equity (re) for a closely-held business is the basic “build-up” method, or a similar variation (e.g, Trevino, 1997, Pinto, 2020; Damodaran, 2024b). Dre = Risk Free Rate + Equity Risk Premium + Industry Premium + Firm Specific Premium + Size Premium In the build-up approach, the risk-free rate is generally determined by the yield rate of a government backed instrument, such as T-bills or T-bonds, although there is some debate as to which is most appropriate. The calculation of the equity risk premium can be quite complicated, with different opinions regarding the appropriate methodology. Inevitably, however, the equity premium is calculated from data of publicly-traded firms. Fortunately for the business appraiser, the calculated equity risk premiums are easily obtained from published sources, such as from Kroll (Kroll, 2024) or by Professor Aswath Damodaran’s work at New York University (Damodaran, 2024). Kroll, for example, currently reports a 5.0% equity premium for 2024 when developing a discount rate for U.S. based firms. The equity premium for international markets can also vary dramatically based on the country’s risk and credit profile. Damodaran (2024a), for example, reports a 2023 equity risk premium of 15.43% for Egypt, and 8.70% for Spain, while other countries such as Canada and Germany are almost identical to the U.S. Since equity premiums are almost always determined from averages obtained from the full equity markets, when developing an appropriate discount rate for a particular target firm, consideration must then be given more specific characteristics, such as industry differences and firm size adjustments. Industry premiums are also available from a variety of sources, such as Damodaran (2024a). If the target firm is a small firm, however, the issue of an appropriate small firm premium in determining the discount rate must be given serious consideration. That is the focus of this study. 2. Commonly Used Size Premiums: Publicly-Traded Firms The relationship between the size of the firm and the value of the firm has received significant attention. From a theoretical point of view, the argument is basically two-fold. First, larger firms are believed to have more bargaining and negotiating power in the market with their upstream suppliers and downstream customers. The issue of asymmetric bargaining power enjoyed by larger firms has been discussed for decades in the industrial organization and strategic management fields under various headings, such as “vertical quasi-integration” and “bilateral market power” (Blois, 1972; Galbraith and Stiles, 1983; Galbraith and DeNoble, 1992; Porter, 1976). Interest in the impact of asymmetric bargaining power on supply chain relationships continues to the present time, with empirical research consistently showing significant cost/price advantages for larger firms. (e.g., Picot et al, 2023; Chi and Goo, 2023; Jo, Jeong and Kim, 2023). Second, large firms are believed to have 32The Journal of Entrepreneurial Finance, Vol. 27, Iss. 1 [2025], Art. 2 https://digitalcommons.pepperdine.edu/jef/vol27/iss1/2 DOI: 10.57229/2373-1761.1498 scale advantages both in input components, such as hiring better workers and receiving bulk discounts, and in output components, such as size advantages in distribution and product placement. The impacts of both of these forces, market power and scale economies, should be reflected in the firm’s earnings. The impact of firm size on the cost of equity has been almost exclusively examined with publicly-traded firms, as revealed by the size premium published by various financial data providers, such as Kroll (2024), Duff and Phelps (2015-2017) and Ibbotson (Ibbotson and Harrington, 2020). Contrary to the findings of a disappearing size effect that some early research indicated (e.g., Foerster and Porter, 1992; Horowith, Loughran and Savin, 2000) there is substantial evidence that a small firm risk premium does exist with publicly-traded firms, in both the U.S. and international markets (e.g., Amel-Zadeh, 2011; Elyasiani, Gambarelli, and Muzzioli, 2020; Yadav, Pahi and Gangakhedkar, 2022; Kroll, 2024; Ibbotson and Harrington, 2020; Khan, Hassan and Ali, 2012). For years, Kroll (which merged with Duff and Phelps in 2018) and other financial data providers have calculated the size premium using various risk adjusted stock price data categorized by the size deciles of publicly-traded firms, with the 10th decile being the smallest 10% of the publicly-traded firms examined. When valuing a small closely-held firm, however, there is a problem with using this “decile” premium - the average size of firms in the 10th decile of publicly-traded firm is approximately $30million in market capitalization. In comparison, the vast majority of closely-held firms have market capitalizations significantly less, particularly if the target firm is a typical owner-operated business. In fact, the median market value in the DealStat databases of closely-held firm sales transactions from 2020 to 2024 was approximately $400,000; with average market values ranging somewhat higher or lower depending on the industry sector. Comparing a small closely-held firm even with the 10th decile of publicly-traded firms is like comparing apples and oranges, at best. Recognizing this, Kroll and others, now report using four, more detailed 10th decile categories in their analysis of U.S. publicly-traded firms - 10z, 10y, 10x, and 10w, with 10z being the smallest. According to recent Kroll calculations, the small firm premiums for these the different categories of publicly-traded U.S. firms are shown below for 2021 and 2022. While the small firm premium can vary from year to year (declining slightly somewhat in the last decade for all deciles) it has been relatively stable at the smallest category, 10z. For example, from 2012 to 2022 the Kroll 10z size premium has ranged from a high of 11.77% (2012) to 11.17% (2022). Table 1 shows the Kroll small firm decile calculations for 2021 and 2022. Table 1: Size Premiums for Publicly-Traded Firms – Kroll Categories of Market Capitalization Firm Size Category Mid-Point Capitalization 2022 2021 10z $6,915,000 11.17% 11.29% 10y $15,920,000 6.34% 6.60% 10x $22,100,000 4.54% 4.65% 10w $27,035,000 2.34% 2.60% 9 $45,890,000 2.10% 2.29% 8 $96,755,000 1.21% 1.46% 7 $173,545,000 1.34% 1.54% 6 $272,345,000 1.18% 1.37% 5 $414,235,000 0.89% 1.09% 4 $661,625,000 0.65% 0.75% 3 $1,247,740,000 0.55% 0.71% 2 $2,642,930,000 0.43% 0.49% However, even the 10z category, which reports the smallest publicly-traded firms, has a midpoint equity capitalization near $7million, which is still many times larger than the average 33 Galbraith: Size Premium in Small Business ValuationPublished by Pepperdine Digital Commons, 2025 capitalization reported in the databases of closely-held firm sales transactions. However, the vast majority of small business appraisers are taught in their training classes to use the 10z (some still just use the 10 category) to determine the small firm equity premium. When valuing a typical closely-held business with a much smaller capitalization, an obvious problem is evident - one can see a clear non-linear growth in the size premium as the firm gets smaller (Table 1 and Figure 1). It is also evident from the decile calculations that the dramatic increase in size premiums appear to occur primarily in the smallest size categories. This also indicates that even the more detailed decile categorization may not capture the appropriate size premium for the smallest firms, particularly if they fall in the lower capitalization range of the 10z definition. Figure 1: Reported Small Firm Equity Premiums: Kroll Categories 6-10z (Average 2021 & 2022) 3. Analyzing the Size Premium: Publicly-Traded Firms We approach the problem of estimating a more accurate small firm premium for very small, closelyheld firms in several ways. First, for comparison purposes we simply use a regression of the Kroll data. We attempted several different models (linear, logarithmic, exponential, power curve) and using different Kroll categories. Since this is an exercise in extrapolation, obtaining a model with a good fit (or R2) is critical. After attempting several different model specifications, we found that a logarithmic regression model using the midpoint capitalization for the 7,8,9, 10w, 10x, 10y, and 10z categories provides a good fit (R2 = 0.775). A similar model was found using the 2 to 10z categories, although the R2 was not as high, while the 9 to 10z categories provided a slightly better fit (R2 = 0.859), but with fewer data points. For the size premium metric for this analysis, we average the 2021 and 2022 data. It should be noted that while there are only technically seven data points in our regression, each of the Kroll categories is made up of hundreds of firms, for a total of approximately 2,000 publiclytraded firms for the categories 7 to 10z. The results of the logarithmic model are shown below. Table 2: Logarithmic Model, Small Firm Premium – Kroll Categories of Market Capitalization, 7 to 10z Variable B T-statistic Prob Constant 14.427 5.650 <0.002 Ln(Firm Capitalization) -2.891 -4.148 <0.009 34The Journal of Entrepreneurial Finance, Vol. 27, Iss. 1 [2025], Art. 2 https://digitalcommons.pepperdine.edu/jef/vol27/iss1/2 DOI: 10.57229/2373-1761.1498 To see the difference, if we assume a firm has an approximate $300,000 equity capitalization, using our first logarithmic regression model a firm of this size would have a small firm premium of 17.91% versus 11.17% if one simply uses the 2022 10z category from Kroll. This significantly changes the overall discount rate calculations, which would have a major impact on the estimated market value of the target firm. However, while the data from publicly-traded firms certainly suggest a non-linear relationship between firm size and its equity premium, there are the typical validity concerns about extrapolating a model fitted to a particular set of data to forecast something outside the range of the original data set or scope. While intuitively attractive, the risks of making predictions beyond the range of the data used to estimate the original model are well known, not only in finance but many other fields such as ecology, epidemiology and engineering. This is often called a “transportability” or generalizability validity problem where the study sample does not overlap with the target population (Lesko et al, 2020), that is, in our case, the much smaller size range of closely-held firms. In order to address this extrapolation validity issue, simulation studies are often suggested (e.g, Bartley et al, 2019). Another option is to analyze highly comparable or representative datasets that cover the data range of interest (e.g., Smith, 2019), thus bringing the treatment of external validity in line with internal validity (e.g., Lesko et al, 2020). In this paper, we are therefore interested in exploring whether the same non-linear, negative small size premium continues for smaller, closely-held firms. This is our interest for two reasons – first, to address the validity of extrapolating size premium determined from much larger publicly-traded data to much smaller, closely-held firms, and second, to develop a similar model of size premiums using actual transaction data for small closely-held firms. 4. The Impact of Size: Closely Held Firms It is impossible to exactly replicate the analysis of publicly-traded firm size premiums with transaction data for closely-held firms for several reasons. First, unlike publicly-traded firms where daily stock prices can be examined for risk-adjusted market returns, closely-held firm transaction data is only a one-time event upon the sale of the business. Given this, our analysis cannot calculate a beta-adjusted risk associated with the small size premium. However, transaction data does represent the only fair market value determination for closely-held firms. Second, as previously mentioned, normally transaction data for a closely-held firm is reported as a “market” value or a “transaction price”. A market value or transaction price represents the total price of the deal, excluding any debt and cash (since debt and cash are rarely assumed during the sale of a closely-held firm). This is similar to a real estate sale, where a house is sold and subsequently recorded in the real estate transaction databases at a price that doesn’t incorporate any outstanding mortgage against the property. On the other hand, the analysis of publicly-traded firm data, including the Kroll data, is based on stock price data, which is an “equity” value. Third, in any closely-held company the owners can significantly influence reported earnings, particularly related to control over salaries paid to themselves. For example, some owners of closely held firms may pay themselves a large salary, thus reducing reported earnings, while other owners of closely held firms may not pay themselves a salary, thus resulting in higher reported earnings and taking personal income through owner “draws”. When performing a business valuation using the firm’s earnings, it often becomes necessary to normalize the financial statements to reflect what an arms-length investor might do if they were to invest-in, or purchase, the company. However, we are not interested in exactly replicating the analysis from publicly-traded firms, but rather interested in two issues. Our first interest, and the focus of Analysis 1, is determining whether small, closely-held firms follow the same non-linear, logarithm pattern as seen in Table 2 using 35 Galbraith: Size Premium in Small Business ValuationPublished by Pepperdine Digital Commons, 2025 comparable metrics. If closely-held small firms follow the same pattern as seen for publicly-traded firms, then we have addressed the major validity concerns regarding the extrapolation of the estimated logarithm regressions for the larger firm categories such as shown in the Kroll calculations. Second, using transaction data for closely-held firms, can we develop a model that does, in fact, reasonably estimate the size premium in determining the cost of equity discount rate for smaller firms? This is the focus of Analysis 2. 5. Data To examine this relationship for closely-held firms, data was obtained from a proprietary database of sales transactions for closely-held firms. We use the DealStat’s database. DealStat (formally Pratt’s Stats) is the world’s largest database of sales transactions for closely-held firms. Data comes from a variety of sources, including business brokers and merger and acquisitions professionals. The transaction data contains several types of information related to each transaction, including the market price, the deal structure, the NAICS codes, product description, and the number of employees. Also included are revenue, income and sometimes balance sheet items. The firms include a broad array of businesses, with the vast majority of firms under $10million in revenues. We used sales transactions for the years 2016 to 2019, and 2022 to 2024. We exclude 20202021 to control for the impact of the Covid-19 years. There is ample evidence that most small businesses were dramatically impacted by the Covid-19 restrictions of 2020, while 2021 is considered a year of pent-up demand for many industry sectors (Dore and March, 2022). We examined the broad manufacturing, retail, and wholesale industry sectors (NAICS 31, 32, 33, 42, 44, 45), resulting in a total sample size of 2,092. We examined these sectors since these industries are relatively stable, they are not as strongly influenced by personal goodwill components such as the various services sectors, and they are not heavily regulated, such as utilities. While recognizing there are probably industry specific differences, since Kroll (and other financial service providers) pool data for their reported size premiums, and since business valuators look for a generalized small firm premium in their analysis, we also pool these sectors for the present analysis. We perform two different analyses. The first analysis (Analysis 1) examines whether very small, closely-held firms follow the same non-linear, logarithm pattern as seen in studies of publicly-traded firms. This analysis is designed to address the validity concerns regarding the extrapolation of the estimated logarithm regressions for the larger firm categories. The second analysis (Analysis 2) develops a model that reasonably estimates the size premium in determining an equity-based discount rate for smaller firms using a subset of the transaction data. 6. Analysis 1: Small Size and Sellers Discretionary Cashflow Capitalization Rates For our first analysis, we are initially interested in the “shape” of the relationship between firm size, as measured by market value or transaction price, and a reasonably comparable measure of value. This specifically addresses the validity issue of extrapolating small firm premium estimates from models developed from publicly-traded firm data. To control for the issue of owner’s salary identified above, we use a seller’s discretionary cash flow measure, or SDCF (combination of net earnings, owner’s compensation, and non-cash charges, such as depreciation). The SDCF model is attractive since it is both a commonly used metric for valuing small, closelyheld firms and is regularly recorded in transaction databases of closely-held firms. We then divide SDCF by the transaction price to obtain a SDCF capitalization rate (SDCF CapRate). The SDCF CapRate is 36The Journal of Entrepreneurial Finance, Vol. 27, Iss. 1 [2025], Art. 2 https://digitalcommons.pepperdine.edu/jef/vol27/iss1/2 DOI: 10.57229/2373-1761.1498 therefore similar to an earnings capitalization rate, which divides a firm’s adjusted earnings by the firm’s equity price but rather uses a total owners cashflow measure. Figure 2 shows the plot of our full sample, using the market value or transaction price for the size dimension and the SDCF CapRate. This graph appears to clearly indicate the same non-linear negative relationship between firm size and a capitalization rate measure as seen in the publicly-traded data examined earlier. Figure 2: SDCF CapRates versus Firm Market Value: Small Closely-Hold Firms We then calculated both a linear regression and a logarithm regression. For the firm size dimension, we again use the actual transaction price or market value. However, about 10% of the transactions in the database also provide balance sheet data for the firm. For these firms it is also possible to calculate an approximation of total firm equity value by simply subtracting long-term debt from the transaction price/market value. This firm total equity value is similar to the “capitalization” terminology of firm size commonly used for publicly-traded firms. We controlled for possible outliers by limiting SDCF CapRates greater than 10% (or Transaction Price/SDE multiples<10), since 97% of the calculated SDCF multiples are less than 10). This also controls for firms reporting little or no positive cash flow, or possibly mis-entered data. We also did not include firms designated as “development stage firms”, since a capitalization of earnings or cashflow approaches would generally not be appropriate for these types of firms. Since we are interested in the size impact for small firms, we only examined U.S. firms with market values less than $10million, purposely resulting in some overlap with the 10z category of publicly-traded firms. Table 3 shows the results of our regression analysis. 37 Galbraith: Size Premium in Small Business ValuationPublished by Pepperdine Digital Commons, 2025 industries also exhibit a similar relationship between size and firm premiums for determining an appropriate earnings discount rate, we did not include them in our model estimates. 44The Journal of Entrepreneurial Finance, Vol. 27, Iss. 1 [2025], Art. 2 https://digitalcommons.pepperdine.edu/jef/vol27/iss1/2 DOI: 10.57229/2373-1761.1498 References Amel-Zadeh, A. (2011). The return of the size anomaly: Evidence from the German stock market. European Financial Management, 17(1), 145-182. Bartley, M., Hanks, E., Schliep, E., Soranno, P., & Wagner, T. (2019). 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The nexus between firm size, growth and profitability: New panel data evidence from Asia–Pacific markets. European Journal of Management and Business Economics, 31(1), 115-140. 46The Journal of Entrepreneurial Finance, Vol. 27, Iss. 1 [2025], Art. 2 https://digitalcommons.pepperdine.edu/jef/vol27/iss1/2 DOI: 10.57229/2373-1761.1498