<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">TEL</journal-id><journal-title-group><journal-title>Theoretical Economics Letters</journal-title></journal-title-group><issn pub-type="epub">2162-2078</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/tel.2023.133034</article-id><article-id pub-id-type="publisher-id">TEL-126013</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Business&amp;Economics</subject></subj-group></article-categories><title-group><article-title>
 
 
  Cost of Capital for Private Firms
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Federico</surname><given-names>Beltrame</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Luca</surname><given-names>Grassetti</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Gianni</surname><given-names>Zorzi</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib></contrib-group><aff id="aff2"><addr-line>Department of Management, Ca’ Foscari University, Venice, Italy</addr-line></aff><aff id="aff1"><addr-line>Department of Economics and Statistics, University of Udine, Udine, Italy</addr-line></aff><pub-date pub-type="epub"><day>18</day><month>05</month><year>2023</year></pub-date><volume>13</volume><issue>03</issue><fpage>535</fpage><lpage>548</lpage><history><date date-type="received"><day>29,</day>	<month>March</month>	<year>2023</year></date><date date-type="rev-recd"><day>27,</day>	<month>June</month>	<year>2023</year>	</date><date date-type="accepted"><day>30,</day>	<month>June</month>	<year>2023</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  This paper elaborates 
  on 
  a new default-based cost of capital estimation for
   private-held firms. We test the model
  ’s
   ability to incorporate systematic
   risk and size premium. Results highlight a positive and statistically significant effect of CAPM expected return and size premiums on this novel cost of capital measure. Beyond the utility in practice for private equity valuation, preliminary results are promising for application on a larger cross-country sample.
 
</p></abstract><kwd-group><kwd>Size Premium</kwd><kwd> Cost of Capital</kwd><kwd> Default Risk</kwd><kwd> Private Firms</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>Most empirical studies on the cost of equity determinants focus on listed firms (see  Wan, 2020  and  Hmiden et al., 2022  among others) and, apart from comparable approaches  (Abudy et al., 2016;   Barg et al., 2021) , private firms’ cost of capital investigations are lacking.</p><p>This paper elaborates on a new default-based cost of capital estimation for private-held firms, implying the default probability of Italian Guarantee Fund rating. We test the ability of the model to incorporate both systematic risk and size premium, analyzing a sample of Italian equity valuation reports. We imply all the publicly available reports with sufficient data for determining the discount rate used in the estimation (43 documents). The sample size is in line with other studies on private firm valuation (see, for example  Elnathan et al., 2010 , based on 66 firms).</p><p>Results highlight a positive and statistically significant effect of CAPM expected return and size premiums on this novel cost of capital measure.</p><p>In the knowledge of authors, no attempts are given by literature relatively on the effect of size premium and systematic risk on the privately-held firm cost of capital. However, beyond the utility in practice for private equity valuation, preliminary results are promising for application on a larger cross-country sample.</p><p>The paper is structured as follows. Section 2 elaborates on the default-based cost of capital estimation and hypotheses. Section 3 presents the sample and the research design, while Section 4 reports the results. Section 5 concludes.</p></sec><sec id="s2"><title>2. The Cost of Capital Estimation and Hypotheses</title><p>Private firms’ cost of capital estimation is usually based on comparable stock data (  Abudy et al., 2016  among others) or implies credit risk measures  (Oricchio, 2012) . An exception is the model of  Cheung (1999)  which is based on the same default probability, both for equity holders and debt-holders. However, these two categories have a different risk profiles. As a response, the following model recognizes the different risk positions for equity in respect of debt financing at the probability of default level.</p><p>In accordance with past literature  (Solomon, 1963;   Baxter, 1967;   Turner, 2014) ,</p><p>the basic idea is that for extremely high leverage ratio ( D V → 1 , E → 0 ), the cost</p><p>of debt approximates the cost of capital ( r D → r 0 ). As a consequence, the cost of capital determination is just a special case of cost of debt estimation  (Beltrame &amp; Zorzi, 2022) .</p><p>Given a certain stream of operating cash flows:</p><p>( F 0 o p , F 1 o p , ⋯ , F i o p , ⋯ , F N o p ) (1)</p><p>where a generic firm operating cash flow F i o p can be viewed as the sum of equity cash flow and debt cash flow, since the part of operating cash flow not servicing the debt is distributed to equity-holders:</p><p>F i o p = F i E + F i D (2)</p><p>In the following, we report the assumptions for determining the cost of capital.</p><p>Assumption I: F i E = 0 for every i.</p><p>In order to set F i E = 0 , F i D → F i o p , thus F i o p = F i D .</p><p>The equality can be re-written, decomposing both F i o p and F i D :</p><p>E B I T i − Δ I C i = I E i − Δ B V D i (3)</p><p>where EBIT (Earning before interests and taxes) is the firm operating income, IE are the interest expenses, ∆IC is the variation in invested capital and ∆BVD is the variation in the book value of financial debt.</p><p>Assumption II: I E i → E B I T i and Δ B V D i → Δ I C for every i.</p><p>Imposing this restrictive assumption, we are able to extend F i E = 0 both for a stable stream of cash flows (steady-state framework) and for a time-varying cash flows. Note that in time = 0, the assumption II implies B V D 0 = I C 0 , since Δ B V D 0 = B V D 0 and Δ I C 0 = I C 0 .</p><p>A null F i E from i = 0 to i = N, both in steady state and non-steady state framework, implies an equity value equal to zero. And, as a consequence, an equity value equal to zero leads to r 0 = r D . Using the WACC formulae, for simplicity with no taxes, we have:</p><p>W A C C = r 0 = r E E V + r D D V = r E 0 D + r D D D = r D (4)</p><p> Copeland et al. (2005)  obtain the same result both with and with no taxes using a structural model.</p><p>Exploiting a risk-neutral framework and a recovery rate on equity equal to zero as in  Cheung (1999) , the cost of debt will be:</p><p>r D = r f + P D 1 − P D (5)</p><p>where r f is the risk-free rate and PD is the probability of default.</p><p>In the same way, we can estimate the unlevered cost of capital under Assumptions I and II:</p><p>r D , I , I I = r 0 = r f + P D I , I I 1 − P D I , I I (6)</p><p>where P D I , I I is the probability of default calculated under I and II.</p><p>Our cost of capital estimation is directly dependent on P D I , I I as a measure of default risk. Empirical literature shows that credit risk is affected by both idiosyncratic firm characteristics and systematic factors  (Denis &amp; Denis, 1995;   Jorion &amp; Zhang, 2009) . This evidence leads to our first hypothesis:</p><p>H1. Systematic risk positively affects r D , I , I I .</p><p>Regarding the specific risk-cost of capital evidences, the size premium  (Banz, 1981;   Fama &amp; French, 1992)  can be shown as an additional idiosyncratic component rather than a systematic risk one  (Lamoureux &amp; Sanger, 1989) . Extending the database of  Fama and French (1992)  to 2000 and implying a Fama-MacBeth regression,  Malkiel and Xu (2004)  show how an idiosyncratic risk measure absorbs the size effect. Since the cost of debt usually prices specific firm characteristics, we can formulate our second hypothesis:</p><p>H2. Size premium positively affects r D , I , I I .</p></sec><sec id="s3"><title>3. Research Design, Sample and Cost of Capital Variable</title><sec id="s3_1"><title>3.1. Research Design</title><p>Our empirical analysis aims to test whether the measure of the cost of capital presented in the previous section can price both the systematic risk and size premium components. The deterministic part of the model can be defined as follows:</p><p>TLA_CoC = g ( Systematic_CoC , Size_premium , Firm_size , Other_FixedEffects ) (7)</p><p>where g ( ⋅ ) is a generic link function.</p><p>In <xref ref-type="table" rid="table1"><xref ref-type="table" rid="table">Table </xref>1</xref>, variables definitions and sources are reported.</p><p>The other fixed effects consider Sector (Industrial, Services, Commercial, Real estate, and Constructions) and year of observation.</p><table-wrap id="table1" ><label><xref ref-type="table" rid="table1"><xref ref-type="table" rid="table">Table </xref>1</xref></label><caption><title> Variable definitions and sources</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Variable</th><th align="center" valign="middle" >Description</th><th align="center" valign="middle" >Source</th></tr></thead><tr><td align="center" valign="middle" >TLA_CoC</td><td align="center" valign="middle" >The TLA_CoC indicates the alternative cost of capital measure based on a default probability of a fully levered firm and on a certain level of risk-free-rate used by analysist in the firm valuation. More in detail, the cost of capital is operationalized in four steps: 1) We calculate the ratios reported in the second column of the appropriate table in appendix (looking at the firm sector), linking coefficients, floor and cap to each ratio value; 2) We perform Equation (10) to have a final score; 3) Basing on the score range we associate the PD through <xref ref-type="table" rid="table2"><xref ref-type="table" rid="table">Table </xref>2</xref> data; 4) Taking the risk-free selected by the expert in the valuation report and the PD we calculate the cost of capital through Equation (6).</td><td align="center" valign="middle" >Equity valuation reports and Amadeus Aida data base</td></tr><tr><td align="center" valign="middle" >Systematic_CoC</td><td align="center" valign="middle" >The Systematic_CoC is the CAPM-based calculation of the unlevered cost of capital. Unfortunately, in some reports Betas and market risk premium inputs are not indicated. The unlevered cost of capital is extrapolated from the firm equity value and the WACC or the Cost of equity, accordingly to Modigliani and Miller (1963) : W A C C = r 0 ( 1 − D V t c ) → r 0 = W A C C ( 1 − D V t c ) , r E = r 0 + ( r 0 − r D ) D E ( 1 − t c ) → r 0 = r E + r D D E ( 1 − t c ) 1 + D E ( 1 − t c ) .</td><td align="center" valign="middle" >Equity valuation reports</td></tr><tr><td align="center" valign="middle" >Size_premium</td><td align="center" valign="middle" >The Size_premium is the spread applied by accounting experts in the equity report to price the firm size effect.</td><td align="center" valign="middle" >Equity valuation reports</td></tr><tr><td align="center" valign="middle" >Firm_size</td><td align="center" valign="middle" >Firm_size is the control variable and takes the value of the logarithm of assets in model 2 and the logarithm of revenues in Model 3.</td><td align="center" valign="middle" >Equity valuation reports</td></tr></tbody></table></table-wrap><p>This table reports the variables used in the empirical analysis. Fixed effects are on Sector (Industrial, Services, Commercial, Real estate and Constructions) and year.</p><p>The model in Equation (7) considers a percentage measure as the response variable. For this reason, the classical linear model specification cannot be directly applied. We finally decided to consider a Beta regression as proposed by  Ferrari and Cribari-Neto (2004) . The parameterization proposed by these authors accounts for the specific behavior of the dependent variable. Y is supposed to be Beta distributed:</p><p>y ~ B ( μ , ϕ ) with 0 &lt; y &lt; 1 , (8)</p><p>where μ ∈ ( 0 , 1 ) is the expected value for the distribution. The variance V A R ( y ) = μ ( 1 − μ ) / ( 1 + ϕ ) depends on both μ and ϕ &gt; 0 which represents the dispersion parameter (the larger it is the smaller the variance observed in the data). For Beta distribution, the variance of the response variable is a function of μ . This characteristic renders the regression model based on this parameterization is heteroskedastic.</p><p>The model, as in the generalized linear model class, considers the estimation of the population mean based on a link function that we considered to be the logit transformation and, in its basic formulation, presents a fixed dispersion parameter. The logit link function is as follows:</p><p>g ( μ ) = log ( μ 1 − μ ) . (9)</p><p>The estimated parameters can be interpreted as log-odds ratios connected to the explicative variables given the model specification. In short, positive values correspond to a positive effect on the odds values and, consequently, on the estimated proportion (percentage). Negative parameters can be interpreted specularly.</p><p>The model estimation is obtained considering the maximum likelihood approach using R statistical software  (R Core Team, 2022)  and, in particular, “betareg” library described in  Cribari-Neto and Zeileis (2010) .</p></sec><sec id="s3_2"><title>3.2. Sample</title><p>The financial data is hand collected, using Italian data of equity valuation reports of accounting experts. We explore and collect data on Google, digiting the appropriate keywords: we write “valutazione” (valuation), “perizia” (appraisal) and “capitale economico” (equity value), going until the last page of the Google results. We use all the utilizable reports available from 2003 to 2022, collecting 43 observations. It was often necessary to complete the reports using the financial data from the AIDA database.</p></sec><sec id="s3_3"><title>3.3. The PD<sub>I</sub>,<sub>II</sub> Determination through the Italian Guarantee Fund Rating</title><p>The Guarantee Fund for SMEs is an instrument set up by the Italian Ministry of Economic Development through Law no. 662/96 to facilitate access to credit for small businesses. This support is favored through the concession of a public guarantee that replaces collateral and personal guarantees normally provided by companies and entrepreneurs. Guarantees are granted after a rating assessment, substantially in line with the rating systems commonly used by credit intermediaries (financial ratios, corrected for bank relationships’ elements and other warning events). It is possible to elaborate a rating and a PD just through the financial ratios, calibrated for considering firm’s legal form (sole owner firm, non-limited company and limited company), accounting type (simplified or ordinary) and sector (industrial firm, constructions, commercial firm, services and real estate). The financial ratios-based rating is the result of four steps:</p><p>1) Financial and economic ratios calculation;</p><p>2) Ratios normalization (i.e. to normalize a ratio denominator equal to zero);</p><p>3) Dummy calculations;</p><p>4) Final score calculation (the system multiplies normalized ratios/dummies and coefficients to obtain the total score). In formulas:</p><p>Firmscore = Constant + ∑ i = 1 N Variable i &#215; Coefficient i (10)</p><p>The firm score can be obtained through the use of a platform made available by the fund (https://fdg.mcc.it/rating/) or using the formulas reported in this Italian guarantee fund technical document: https://www.fondidigaranzia.it/wp-content/uploads/2019/12/Specifiche-tecniche-per-il-calcolo-della-probabilit&#224;-di-inadempimento-dal-20200215.pdf. In Appendix, we report <xref ref-type="table" rid="table">Table </xref>A1, where we provide all the details useful for the score computation for each sector: constant, variables and coefficients for firm forms and sectors composing the sample of the study. The tables also report the scores under Assumptions I and II. Finally, the P D I , I I can be associated by looking at the correspondences in <xref ref-type="table" rid="table2"><xref ref-type="table" rid="table">Table </xref>2</xref>.</p><table-wrap-group id="2"><label><xref ref-type="table" rid="table2"><xref ref-type="table" rid="table">Table </xref>2</xref></label><caption><title> Scoring, probability of default of the Italian Guarantee Fund and descriptive statistics</title></caption><table-wrap id="2_1"><table><tbody><thead><tr><th align="center" valign="middle" >Rating</th><th align="center" valign="middle" >Score Range (low)</th><th align="center" valign="middle" >Score Range (High)</th><th align="center" valign="middle" >PD</th></tr></thead><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >−999,999</td><td align="center" valign="middle" >−4.7066745760</td><td align="center" valign="middle" >0.12%</td></tr><tr><td align="center" valign="middle" >2</td><td align="center" valign="middle" >−4.7066745760</td><td align="center" valign="middle" >−4.4338240620</td><td align="center" valign="middle" >0.33%</td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >−4.4338240620</td><td align="center" valign="middle" >−4.2547779080</td><td align="center" valign="middle" >0.67%</td></tr><tr><td align="center" valign="middle" >4</td><td align="center" valign="middle" >−4.2547779080</td><td align="center" valign="middle" >−3.8889098170</td><td align="center" valign="middle" >1.02%</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >−3.8889098170</td><td align="center" valign="middle" >−3.4677848820</td><td align="center" valign="middle" >1.61%</td></tr><tr><td align="center" valign="middle" >6</td><td align="center" valign="middle" >−3.4677848820</td><td align="center" valign="middle" >−3.2130939960</td><td align="center" valign="middle" >2.87%</td></tr><tr><td align="center" valign="middle" >7</td><td align="center" valign="middle" >−3.2130939960</td><td align="center" valign="middle" >−2.8844139580</td><td align="center" valign="middle" >3.62%</td></tr><tr><td align="center" valign="middle" >8</td><td align="center" valign="middle" >−2.8844139580</td><td align="center" valign="middle" >−2.6198046210</td><td align="center" valign="middle" >5.18%</td></tr><tr><td align="center" valign="middle" >9</td><td align="center" valign="middle" >−2.6198046210</td><td align="center" valign="middle" >−2.1981980800</td><td align="center" valign="middle" >8.45%</td></tr><tr><td align="center" valign="middle" >10</td><td align="center" valign="middle" >−2.1981980800</td><td align="center" valign="middle" >−1.5324805970</td><td align="center" valign="middle" >9.43%*</td></tr><tr><td align="center" valign="middle" >11</td><td align="center" valign="middle" >−1.5324805970</td><td align="center" valign="middle" >999,999</td><td align="center" valign="middle" >16.30%*</td></tr></tbody></table></table-wrap><table-wrap id="2_2"><table><tbody><thead><tr><th align="center" valign="middle" >Variable</th><th align="center" valign="middle" >Mean</th><th align="center" valign="middle" >Median</th><th align="center" valign="middle" >St. Dev.</th><th align="center" valign="middle" >Min</th><th align="center" valign="middle" >Max</th></tr></thead><tr><td align="center" valign="middle" >TLA_Coc</td><td align="center" valign="middle" >0.077</td><td align="center" valign="middle" >0.067</td><td align="center" valign="middle" >0.040</td><td align="center" valign="middle" >0.021</td><td align="center" valign="middle" >0.200</td></tr><tr><td align="center" valign="middle" >Systematic_CoC</td><td align="center" valign="middle" >0.066</td><td align="center" valign="middle" >0.068</td><td align="center" valign="middle" >0.020</td><td align="center" valign="middle" >0.025</td><td align="center" valign="middle" >0.100</td></tr><tr><td align="center" valign="middle" >Size_Premium</td><td align="center" valign="middle" >0.008</td><td align="center" valign="middle" >0.000</td><td align="center" valign="middle" >0.014</td><td align="center" valign="middle" >0.000</td><td align="center" valign="middle" >0.045</td></tr><tr><td align="center" valign="middle" >LnRevenues</td><td align="center" valign="middle" >14.716</td><td align="center" valign="middle" >15.013</td><td align="center" valign="middle" >2.200</td><td align="center" valign="middle" >9.210</td><td align="center" valign="middle" >17.871</td></tr><tr><td align="center" valign="middle" >LnAssets</td><td align="center" valign="middle" >14.883</td><td align="center" valign="middle" >15.175</td><td align="center" valign="middle" >1.969</td><td align="center" valign="middle" >10.644</td><td align="center" valign="middle" >17.867</td></tr><tr><td align="center" valign="middle" >Year</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >2003</td><td align="center" valign="middle" >2021</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >%</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >Sector (composition)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >…Commercial</td><td align="center" valign="middle" >5%</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >…Construction</td><td align="center" valign="middle" >2%</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >…Industrial</td><td align="center" valign="middle" >21%</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >…Real estate</td><td align="center" valign="middle" >2%</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >…Services</td><td align="center" valign="middle" >70%</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr></tbody></table></table-wrap></table-wrap-group><p>The above part is an author elaboration from https://fdg.mcc.it/rating/. The table allows us to link the firm score and the firm score under I and II to PD and PD<sub>I</sub><sub>,II</sub> respectively. *In the absence of non-accounting information, the original model attributes the PD of class 11 (16.30%) to class 10 and introduces a PD of class 12 (22.98%) attributed to class 11. In our empirical analysis, we preferred to keep the PDs of class 10 and 11 without making these adjustments, to avoid anomalous jumps in probability for riskier classes.</p></sec></sec><sec id="s4"><title>4. Results</title><p>On the right, <xref ref-type="table" rid="table2"><xref ref-type="table" rid="table">Table </xref>2</xref> shows a summary description of the involved variables. The main result of this analysis is that data highlights a great presence of services firms in respect of other sectors. For this reason, a dummy variable is implied (1 = Service firm; 0 Otherwise) to better capture the effect and the magnitude of the Services sector. The response variable presents a range of observations that is shrunk toward zero and an approximately symmetric distribution (as suggested by the comparison of mean and median values). Similar behavior is observed for Systematic CoC. Size_Premium shows many null observations. The variables describing the firms’ sizes (LnRevenues and LnAssets) have been transformed by logarithms to solve the asymmetry issues in their distributions, and they present a similar characterization. The Year of observation varies between 2003 and 2021. The number of observations by year ranges from one to eight. For the sake of simplicity, the year is finally considered as a linear trend in the model (but more flexible solutions, such as time polynomials and splines, have been tried too).</p><p><xref ref-type="table" rid="table">Table </xref>3 shows the models’ estimation results. To enhance the model interpretation, we multiplied the observed values of Systematic_CoC and Size_Premium by 100. This way, a unit variation in these variables corresponds to a change by a factor e<sup>β</sup> in the odds. This also can be approximately interpreted as a variation in the probability measure.</p><table-wrap id="table3" ><label><xref ref-type="table" rid="table">Table </xref>3</label><caption><title> Size premium, systematic risk premium and cost of capital</title></caption><table><tbody><thead><tr><th align="center" valign="middle" ></th><th align="center" valign="middle" >(1)</th><th align="center" valign="middle" >(2)</th><th align="center" valign="middle" >(3)</th></tr></thead><tr><td align="center" valign="middle" >(Intercept)</td><td align="center" valign="middle" >74.057*</td><td align="center" valign="middle" >65.373</td><td align="center" valign="middle" >73.519*</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >(41.050)</td><td align="center" valign="middle" >(43.878)</td><td align="center" valign="middle" >(41.088)</td></tr><tr><td align="center" valign="middle" >Year</td><td align="center" valign="middle" >−0.038*</td><td align="center" valign="middle" >−0.034</td><td align="center" valign="middle" >−0.038*</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >(0.020)</td><td align="center" valign="middle" >(0.022)</td><td align="center" valign="middle" >(0.020)</td></tr><tr><td align="center" valign="middle" >Dummy Service = 1</td><td align="center" valign="middle" >−0.124</td><td align="center" valign="middle" >−0.094</td><td align="center" valign="middle" >−0.112</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >(0.157)</td><td align="center" valign="middle" >(0.168)</td><td align="center" valign="middle" >(0.161)</td></tr><tr><td align="center" valign="middle" >LnAssets</td><td align="center" valign="middle" ></td><td align="center" valign="middle" >0.020</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >(0.042)</td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >LnRevenues</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >0.010</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >(0.035)</td></tr><tr><td align="center" valign="middle" >Size_premium</td><td align="center" valign="middle" >0.109**</td><td align="center" valign="middle" >0.109**</td><td align="center" valign="middle" >0.111**</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >(0.052)</td><td align="center" valign="middle" >(0.052)</td><td align="center" valign="middle" >(0.052)</td></tr><tr><td align="center" valign="middle" >Systematic_CoC</td><td align="center" valign="middle" >0.081**</td><td align="center" valign="middle" >0.077**</td><td align="center" valign="middle" >0.077**</td></tr><tr><td align="center" valign="middle" ></td><td align="center" valign="middle" >(0.037)</td><td align="center" valign="middle" >(0.038)</td><td align="center" valign="middle" >(0.039)</td></tr><tr><td align="center" valign="middle" >Pseudo R<sup>2</sup></td><td align="center" valign="middle" >0.234</td><td align="center" valign="middle" >0.240</td><td align="center" valign="middle" >0.237</td></tr></tbody></table></table-wrap><p>The table reports the three models useful to test the effect of systematic and size premium on TLA Cost of capital. Model (1) is with no size effects, (2) with Size = LnAssets and (3) with Size = LnRevenues. ** and * denote statistical significance at the 5% and 10% levels, respectively. Standard errors are reported in parentheses.</p><p>All the models highlight a positive and statistically significant effect of CAPM systematic risk and size premium on the alternative measure of cost of capital (TLA_CoC), confirming hypotheses 1 and 2. Looking at the slope coefficients in the models, a 1% increase in the CAPM cost of capital due to a different business and operating risk profile get an 8.0% - 8.4% increase in the TLA Cost of capital. A similar argumentation can be considered for the Size_premium variable obtaining an estimated positive effect between 11.5% - 11.7%. On average the overall cost of capital is higher with respect to CAPM cost of capital (7.7% versus 6.6%), including both a size premium effect (0.83%) and the rest (7.7% - 6.6% - 0.83%) as a generic idiosyncratic premium.</p><p>The common measures of size cannot catch the true activity dimension and complexity of the firm operating process. Empirical results of our study support this view since (1) the Firm_size never affects the cost of capital, and rather (2) analysts are able to incorporate the true firm size (in terms of operating process, costs, etc.) in the Size_premium, affecting the overall cost of capital.</p><p>Models (1) and (3) highlight a negative relation between Year and TLA_CoC. The TLA_CoC is decreasing during the time range of this study.</p></sec><sec id="s5"><title>5. Conclusion</title><p>The model presented in this paper recognizes the different risk position for equity in respect of debt financing at the probability of default level, exploiting a framework in line with past studies  (Solomon, 1963;   Baxter, 1967;   Copeland et al., 2005;   Turner, 2014;   Beltrame et al., 2014;   Beltrame &amp; Zorzi, 2022) . In addition, we empirically highlight the ability of the model to incorporate both systematic and size premiums.</p><p>Results highlight the usefulness of the model for private equity and investment project valuations. Moreover, these preliminary results could pose the basis for a future large cross-country empirical investigation. A limitation of the study is that the PD calculation model is tailored to Italian SMEs, it should be revised for application in other countries.</p></sec><sec id="s6"><title>Conflicts of Interest</title><p>The authors declare no conflicts of interest regarding the publication of this paper.</p></sec><sec id="s7"><title>Cite this paper</title><p>Beltrame, F., Grassetti, L., &amp; Zorzi, G. (2023). Cost of Capital for Private Firms. Theoretical Economics Letters, 13, 535-548. https://doi.org/10.4236/tel.2023.133034</p></sec><sec id="s8"><title>Appendix</title><p><xref ref-type="table" rid="table">Table </xref>A1 reports the ratios, dummies, and coefficients necessary to obtain the score for a single firm and for each sector. The value of a single ratio/dummy is normalized in term of denominator and range from a floor to a cap reference. The column “Variable under I and II assumptions” report the revised ratio and dummies for a fully levered firm; a net income equal to zero implies interests expenses equal to EBIT, an equity capital equal to zero implies an amount of debts equal to the effective debts plus book value of equity.</p><table-wrap id="table4" ><label><xref ref-type="table" rid="table">Table </xref>A1</label><caption><title> Variables and coefficients by sectors</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Industrial sector</th><th align="center" valign="middle" ></th><th align="center" valign="middle" ></th><th align="center" valign="middle" ></th><th align="center" valign="middle" ></th><th align="center" valign="middle" ></th></tr></thead><tr><td align="center" valign="middle" >Variable</td><td align="center" valign="middle" >Variable under I, II</td><td align="center" valign="middle" >If Denom. = 0 Ratio Equal to:</td><td align="center" valign="middle" >Floor</td><td align="center" valign="middle" >Cap.</td><td align="center" valign="middle" >Coeff.</td></tr><tr><td align="center" valign="middle" >Constant</td><td align="center" valign="middle" >Constant</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−4.584023</td></tr><tr><td align="center" valign="middle" >Current Debts/Revenues</td><td align="center" valign="middle" >Current debts/Revenues</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >0.4</td><td align="center" valign="middle" >1.4</td><td align="center" valign="middle" >1.709764</td></tr><tr><td align="center" valign="middle" >Interests Expenses/EBITDA</td><td align="center" valign="middle" >EBIT/EBITDA</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >−1</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >1.006155</td></tr><tr><td align="center" valign="middle" >Interests Expenses/Debts</td><td align="center" valign="middle" >EBIT/(Debts + Book Value of Equity)</td><td align="center" valign="middle" >0.06</td><td align="center" valign="middle" >0.01</td><td align="center" valign="middle" >0.06</td><td align="center" valign="middle" >21.7339</td></tr><tr><td align="center" valign="middle" >Cash/Revenues</td><td align="center" valign="middle" >Cash/Revenues</td><td align="center" valign="middle" >0.2</td><td align="center" valign="middle" >0.01</td><td align="center" valign="middle" >0.3</td><td align="center" valign="middle" >−3.257.383</td></tr><tr><td align="center" valign="middle" >Revenues/Inventory</td><td align="center" valign="middle" >Revenues/Inventory</td><td align="center" valign="middle" >11</td><td align="center" valign="middle" >1.4</td><td align="center" valign="middle" >11</td><td align="center" valign="middle" >−0.035931</td></tr><tr><td align="center" valign="middle" >% Variation of Revenues − 0.1</td><td align="center" valign="middle" >% Variation of Revenues − 0.1</td><td align="center" valign="middle" >0.2</td><td align="center" valign="middle" >−0.4</td><td align="center" valign="middle" >0.6</td><td align="center" valign="middle" >0.874921</td></tr><tr><td align="center" valign="middle" >Book Value of Equity/Assets</td><td align="center" valign="middle" >Final value = 0</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >0.64</td><td align="center" valign="middle" >−1.842869</td></tr><tr><td align="center" valign="middle" >Dummy = Interest Expenses/ EBITDA If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = EBIT/EBITDA If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−1.380648</td></tr><tr><td align="center" valign="middle" >Dummy = 1 If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = 1 If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >0.502537</td></tr><tr><td align="center" valign="middle" >Dummy = % Variation of Revenues If % Variation of Revenues &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = % Variation of Revenues If % Variation of Revenues &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−1.318575</td></tr><tr><td align="center" valign="middle" >Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise</td><td align="center" valign="middle" >Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >0.925375</td></tr><tr><td align="center" valign="middle" >Current Debts/Revenues &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >Current Debts/Revenues &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−0.672704</td></tr><tr><td align="center" valign="middle" >Interests Expenses/Debts &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >EBIT/(Debts + Book Value of Equity) &#215; (Dummy = 1 if Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−11.51058</td></tr><tr><td align="center" valign="middle" >Cash/Revenues &#215; (Dummy = 1 if Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >Cash/Revenues &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >1.934049</td></tr><tr><td align="center" valign="middle" >Construction Sector</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >Variable</td><td align="center" valign="middle" >Variable under I, II</td><td align="center" valign="middle" >If Denom. = 0 Ratio Equal to:</td><td align="center" valign="middle" >Floor</td><td align="center" valign="middle" >Cap.</td><td align="center" valign="middle" >Coeff.</td></tr><tr><td align="center" valign="middle" >Constant</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−4.258458</td></tr><tr><td align="center" valign="middle" >Interests Expenses/EBITDA</td><td align="center" valign="middle" >EBIT/EBITDA</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >−1</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >0.37765</td></tr><tr><td align="center" valign="middle" >Interests Expenses/Debts</td><td align="center" valign="middle" >EBIT/(Debts + Book Value of Equity)</td><td align="center" valign="middle" >0.01</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >0.03</td><td align="center" valign="middle" >34.64145</td></tr><tr><td align="center" valign="middle" >Book Value of Equity/Assets</td><td align="center" valign="middle" >Final Value = 0</td><td align="center" valign="middle" >0.03</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >2</td><td align="center" valign="middle" >−1.882866</td></tr><tr><td align="center" valign="middle" >Debts/Value of Production</td><td align="center" valign="middle" >(Debts + Book Value of Equity)/ Value of Production</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >1.314629</td></tr><tr><td align="center" valign="middle" >Current Liabilities/Assets</td><td align="center" valign="middle" >Current Liabilities/Assets</td><td align="center" valign="middle" >0.8</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >0.448655</td></tr><tr><td align="center" valign="middle" >Net Income/Value of Production</td><td align="center" valign="middle" >Final Value = 0</td><td align="center" valign="middle" >0.05</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >0.07</td><td align="center" valign="middle" >−5.638927</td></tr><tr><td align="center" valign="middle" >Book Value of Equity/Fixed Assets</td><td align="center" valign="middle" >Final Value = 0</td><td align="center" valign="middle" >3</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >8</td><td align="center" valign="middle" >−0.05176</td></tr><tr><td align="center" valign="middle" >% Variation of Value of Production − 0.1</td><td align="center" valign="middle" >% Variation of Value of Production − 0.1</td><td align="center" valign="middle" >0.2</td><td align="center" valign="middle" >−0.6</td><td align="center" valign="middle" >1.6</td><td align="center" valign="middle" >0.329288</td></tr><tr><td align="center" valign="middle" >Dummy = Interest Expenses/ EBITDA If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = EBIT/EBITDA If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−0.779867</td></tr><tr><td align="center" valign="middle" >Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise</td><td align="center" valign="middle" >Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >0.48568</td></tr><tr><td align="center" valign="middle" >Dummy = % Variation of Value of Production If % Variation of Value of Production &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = % Variation of Value of Production if % Variation of Value of Production &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−0.998434</td></tr><tr><td align="center" valign="middle" >Debts/Value of Production &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >(Debts + Book Value of Equity)/ Value of Production &#215; (Dummy = 1 if Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−0.655727</td></tr><tr><td align="center" valign="middle" >Real Estate Sector</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >Variable</td><td align="center" valign="middle" >Variable under I, II</td><td align="center" valign="middle" >If Denom. = 0 Ratio Equal to:</td><td align="center" valign="middle" >Floor</td><td align="center" valign="middle" >Cap。</td><td align="center" valign="middle" >Coeff.</td></tr><tr><td align="center" valign="middle" >Constant</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−2.569235</td></tr><tr><td align="center" valign="middle" >Interests Expenses/EBITDA</td><td align="center" valign="middle" >EBIT/EBITDA</td><td align="center" valign="middle" >0.8</td><td align="center" valign="middle" >−0.8</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >0.8130648</td></tr><tr><td align="center" valign="middle" >Interests Expenses/Debts</td><td align="center" valign="middle" >EBIT/(Debts + Book Value of Equity)</td><td align="center" valign="middle" >0.01</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >0.06</td><td align="center" valign="middle" >14.0119</td></tr><tr><td align="center" valign="middle" >Book Value of Equity/Assets</td><td align="center" valign="middle" >Final Value = 0</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >−2.721187</td></tr><tr><td align="center" valign="middle" >Value of Production/Current Assets</td><td align="center" valign="middle" >Value of Production/Current Assets</td><td align="center" valign="middle" >1.5</td><td align="center" valign="middle" >0.3</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >−0.1391083</td></tr><tr><td align="center" valign="middle" >Dummy = Interest Expenses/ EBITDA If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = EBIT/EBITDA if EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−1.401464</td></tr><tr><td align="center" valign="middle" >Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise</td><td align="center" valign="middle" >Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−0.5688427</td></tr><tr><td align="center" valign="middle" >Book Value of Equity/Assets &#215; (Dummy = 1 if Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >Final Value = 0</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >1.765224</td></tr><tr><td align="center" valign="middle" >Commercial Sector</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >Variable</td><td align="center" valign="middle" >Variable under I, II</td><td align="center" valign="middle" >If Denom. = 0 Ratio Equal to:</td><td align="center" valign="middle" >Floor</td><td align="center" valign="middle" >Cap.</td><td align="center" valign="middle" >Coeff.</td></tr><tr><td align="center" valign="middle" >Constant</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−1.88977</td></tr><tr><td align="center" valign="middle" >Interests Expenses/EBITDA</td><td align="center" valign="middle" >EBIT/EBITDA</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >−1</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >0.73753</td></tr><tr><td align="center" valign="middle" >Interests Expenses/Debts</td><td align="center" valign="middle" >EBIT/(Debts + Book Value of Equity)</td><td align="center" valign="middle" >0.06</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >0.08</td><td align="center" valign="middle" >16.97147</td></tr><tr><td align="center" valign="middle" >Cash/Revenues</td><td align="center" valign="middle" >Cash/Revenues</td><td align="center" valign="middle" >0.02</td><td align="center" valign="middle" >0.01</td><td align="center" valign="middle" >0.1</td><td align="center" valign="middle" >−3.97341</td></tr><tr><td align="center" valign="middle" >% Variation of Revenues − 0.06</td><td align="center" valign="middle" >% Variation of Revenues − 0.06</td><td align="center" valign="middle" >0.24</td><td align="center" valign="middle" >−0.36</td><td align="center" valign="middle" >0.54</td><td align="center" valign="middle" >1.446892</td></tr><tr><td align="center" valign="middle" >Book Value of Equity/Assets</td><td align="center" valign="middle" >Final Value = 0</td><td align="center" valign="middle" >0.04</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >1.6</td><td align="center" valign="middle" >−2.86327</td></tr><tr><td align="center" valign="middle" >EBITDA/(Interest Expenses + Debts)</td><td align="center" valign="middle" >EBITDA/(EBIT + Debts + Book Value of Equity)</td><td align="center" valign="middle" >0.2</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >0.3</td><td align="center" valign="middle" >−1.68061</td></tr><tr><td align="center" valign="middle" >(Current Assets-Inventory)/ Current Liabilities</td><td align="center" valign="middle" >(Current Assets-Inventory)/ Current Liabilities</td><td align="center" valign="middle" >2</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >2</td><td align="center" valign="middle" >−0.33307</td></tr><tr><td align="center" valign="middle" >Revenues/Assets</td><td align="center" valign="middle" >Revenues/Assets</td><td align="center" valign="middle" >0.9</td><td align="center" valign="middle" >0.5</td><td align="center" valign="middle" >1.7</td><td align="center" valign="middle" >−0.85672</td></tr><tr><td align="center" valign="middle" >Dummy = Interest Expenses/ EBITDA If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = EBIT/EBITDA If EBITDA &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−1.3164</td></tr><tr><td align="center" valign="middle" >Dummy = % Variation of Revenues If % Variation of Revenues &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = % Variation of Revenues If % Variation of Revenues &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−2.98436</td></tr><tr><td align="center" valign="middle" >Interests Expenses/Debts &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >EBIT/(Debts + Book Value of Equity) &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−8.28285</td></tr><tr><td align="center" valign="middle" >Book Value of Equity/Assets &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >Final Value = 0</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >1.368938</td></tr><tr><td align="center" valign="middle" >Revenues/Assets &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >Revenues/Assets &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >0.207691</td></tr><tr><td align="center" valign="middle" >Services Sector</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td></tr><tr><td align="center" valign="middle" >Variable</td><td align="center" valign="middle" >Variable under I, II</td><td align="center" valign="middle" >If Denominator = 0 Ratio Equal to:</td><td align="center" valign="middle" >Floor</td><td align="center" valign="middle" >Cap.</td><td align="center" valign="middle" >Coefficient</td></tr><tr><td align="center" valign="middle" >Constant</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−4.689249</td></tr><tr><td align="center" valign="middle" >Current Debts/Revenues</td><td align="center" valign="middle" >Current debts/Revenues</td><td align="center" valign="middle" >2</td><td align="center" valign="middle" >0.2</td><td align="center" valign="middle" >2.5</td><td align="center" valign="middle" >0.427293</td></tr><tr><td align="center" valign="middle" >Cash/Revenues</td><td align="center" valign="middle" >Cash/Revenues</td><td align="center" valign="middle" >0.04</td><td align="center" valign="middle" >0.01</td><td align="center" valign="middle" >0.16</td><td align="center" valign="middle" >−7.428313</td></tr><tr><td align="center" valign="middle" >% Variation of Revenues − 0.06</td><td align="center" valign="middle" >% Variation of Revenues − 0.06</td><td align="center" valign="middle" >0.14</td><td align="center" valign="middle" >−0.36</td><td align="center" valign="middle" >0.84</td><td align="center" valign="middle" >0.668981</td></tr><tr><td align="center" valign="middle" >Current Liabilities/Assets</td><td align="center" valign="middle" >Current Liabilities/Assets</td><td align="center" valign="middle" >0.8</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >0.82794</td></tr><tr><td align="center" valign="middle" >Interest expenses/Value of Production</td><td align="center" valign="middle" >EBIT/Value of Production</td><td align="center" valign="middle" >0.04</td><td align="center" valign="middle" >0</td><td align="center" valign="middle" >0.04</td><td align="center" valign="middle" >29.88155</td></tr><tr><td align="center" valign="middle" >Debts/Book Value of Equity</td><td align="center" valign="middle" >10 (Since Denominator Is Equal to Zero)</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >−2</td><td align="center" valign="middle" >20</td><td align="center" valign="middle" >0.031407</td></tr><tr><td align="center" valign="middle" >Variable = 1 If Interests Expenses/ EBITDA &lt; 0 and EBITDA &lt; 0; Otherwise Interests Expenses/EBITDA</td><td align="center" valign="middle" >Variable = 1 If EBIT/EBITDA &lt; 0 and EBITDA &lt; 0; Otherwise EBIT/EBITDA</td><td align="center" valign="middle" >Not Nec.</td><td align="center" valign="middle" >Not Nec.</td><td align="center" valign="middle" >Not Nec.</td><td align="center" valign="middle" >0.400514</td></tr><tr><td align="center" valign="middle" >Dummy = % Variation of Revenues If % Variation of Revenues &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >Dummy = % Variation of Revenues If %Variation of Revenues &lt; 0; 0 Otherwise</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−1.558519</td></tr><tr><td align="center" valign="middle" >Current debts/Revenues &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >Current Debts/Revenues &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >−0.245754</td></tr><tr><td align="center" valign="middle" >Cash/Revenues &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" >Cash/Revenues &#215; (Dummy = 1 If Revenues ≤ 500,000; 0 Otherwise)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >5.362561</td></tr><tr><td align="center" valign="middle" >Dummy = 1 If Book Value of Equity &lt; 0; 0 Otherwise</td><td align="center" valign="middle" >0 (Since the Book Value of Equity Is Zero in a Fully Levered Situation)</td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" ></td><td align="center" valign="middle" >0.542214</td></tr></tbody></table></table-wrap></sec></body><back><ref-list><title>References</title><ref id="scirp.126013-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Abudy, M., Benninga, S., &amp; 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