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Database and sample

To show our proposal, we used the SABI database (Iberian Balance Analysis System), which provides financial and accounting information on Spanish companies. We chose reduced size companies in the agrarian sector by following the National Classification of Economic Activities (NACE, 20073). In addition, we selected companies located in the province of Murcia. From this database, we got a sample of 831 agrarian reduced size companies. We eliminated observations relating to companies without available information, with anomalies in their financial statements, for example, negative values in their sales or assets that distort firms’ behavior. Thus, we got a sample of 511 reduced size agrarian companies covering information over the period from 2010 to 2014. Finally, to obtain a homogeneous sample of comparable companies, we selected those companies in the fruit subsector obtaining a final sample of 280 are fruit companies. Table 1 shows the sample distribution for different sizes, sectors and ages.

Table 1. Sample characteristics of agri-food companies in Murcia. Average values (2010-2014) in percentages on the total value.

Small companies account for 61% of the sample. In addition, there is a high percentage of companies that have been in business for less than 25 years. Finally, the productive activity in Murcia is concentrated in the fruit subsector, which represents 54% of the sample.

Variables: Economic valuation based on the DCF model

To evaluate the EV for each company, we applied the DCF model (1) with t = 2015,.., 2019 and l = 5. To estimate the FCFs for the next five years (2015-2019), we determined the evolution of its main components based on the historical sales of each company in the sample and a regression analysis to extrapolate future sales. Once future sales were estimated, FCF (2) were computed by applying the mean of the annual past values of the proportion (ratio) that each FCF component represents with respect to historical sales (Gentry & Reilly, 2007). The discount rate (k) is estimated by applying (5) with the costs of debt (kd), calculated as the ratio of interest expenses to the financial debt of the company. The cost of equity (ke) is computed from (3), where the risk-free rate (Rf) is represented by the 10-year government bond interest rates4. The market risk premium (Pm) is the average historical differential between the market returns and the risk-free rates during the previous years. We obtained these data from Damodaran’s webpage5, which provides the market risk premiums by industry and country. The specific business risk (Pe) was computed by Eq. (4), where the financial profitability of firm i after interest and taxes (i.e., ROE) was obtained from firms’ accounting information and market return values from Damodaran's webpage. Finally, we calculated the residual value (RV) by applying the Gordon model, which assumes that FCFs will grow at a constant rate (g) after the estimation period. Analytically,

where g was assumed to be 1.5%, which was the long-term GDP growth expected for Spain in the next 20 years (PricewaterhouseCoopers, 2013).

Economic value based on spatial information

To illustrate our proposal to determine the SEV, we developed a simulation analysis based on the available sample of agrarian companies. In particular, we selected reduced-sized fruit companies with to obtain a homogeneous sample of comparable firms (Eberhart, 2001). After we selected these companies, we obtained a sample of 280 firms for which we computed the EV by applying the DCF approach. Table 2 shows the EV distribution according to the characteristics of certain firms in the sample.

Table 2. Economic value distribution for the fruit subsector (in logarithm).

Table 2 shows positive relationships of the size and age of the company with economic value. This result coincides with the previous literature, which states that larger and older companies enjoy the advantages of economies of scale and greater market presence, leading to positive results for these companies and higher values (Chen, 2010). The next step was to examine the spatial autocorrelation Moran’s I test for the examined sample. Table 3 shows this result.

Table 3. Moran’s I test for EV.

We found p-values of less than 0.05 with s = 8. There­fore, the null hypothesis of non-spatial autocorrelation was rejected, indicating that fruit firms’ values were related to their neighbours’ economic values when neighbour orders higher than 8 were considered. However, what was the optimum s value to determine spatially comparable companies? To determine the s value that best fits the spatial economic value (SEV) definition (7) and minimizes the absolute difference of EV-SEV, we developed an iterative process that maximizes the spatial autocorrelation structure in the sample by maximizing the significant value for Moran’s I test. By applying this procedure, we determined that s = 11 minimizes the absolute difference between procedures with EV-SEV = 0.0804. Thus, to obtain the SEV for reduced-size fruit companies in Murcia for which there is no available temporal information, we could compute the SEV by applying (7) with s = 11.

Limitations of the spatial economic valuation

Regarding the previous literature, we found that the different valuation models are based, in addition to market characteristics, on the firms’ own characteristics. Thus, an important limitation of the SEV is that it is based only on external information without considering firms’ specific characteristics. Thus, by applying only spatial information, we could obtain a positive valuation of a company that has negative financial ratios. To overcome this limitation, we modified our initial proposal by combining both spatial information and financial information. In particular, we proposed a general spatial specification by defining a spatial first-order autoregressive model with first-order autoregressive disturbances, as in Eq. (9) (LeSage & Pace, 2010).

In this equation, y represents a (280 × 1) vector of the economic valuations from the DCF method for each fruit firm i in the sample, i=1,…,280, and X is the (280×(r+1)) matrix containing a constant term and a set of variables r that takes into account the firm’s financial characteristics. In particular, we include indebtedness as measured by the debt equity ratio (DEBT), which was calculated as total liabilities over total assets. Profitability was computed as the profitability ratio (PROF) with net operating income divided by total assets. Sales growth (CCTO) was computed as the annual sales growth rate, SIZE as the logarithm of total assets, and AGE as the logarithm of the number of years of the company since its constitution. WL and WE were (280×280) spatial contiguity matrices that define the connections between the companies in the sample; u was a (280×1) vector of the spatially correlated residuals, and e is a (280×1) vector of normally distributed errors with mean zero and variance σ2. Spatial interaction effects were tested by the coefficient ρ, which represents the spatial lag coefficient, and λ, which measures the spatial autocorrelation for the residuals u. To estimate this model, we applied the maximum likelihood (ML) (Elhorst, 2010). In addition, we applied the Lagrange multipliers (LM) tests to contrast the spatial structures in the model. The null hypothesis of the LM tests evaluates the absence of spatial correlation. In particular, there are two LM tests, LM-LAG and LM-ERR. The first contrasts the existence of spatial correlation in the dependent variable (WLy), whereas the second (LM-ERR) contrasts the existence of spatial autocorrelation in the error term (WEu) (Anselin et al., 1996). Florax & Former (1992) propose selecting the adequate spatial structure by comparing these LM tests. In this sense, if the LM-LAG is significant and the LM-ERR is not, then the best spatial structure is a spatial autoregressive form in the dependent variable. However, if the LM-ERR is significant and the LM-LAG is not, then the spatial autocorrelation in the error term is considered. Finally, when we obtained significant values in both spatial structures (LM-LAG and LM-ERR), we estimated the model (9). Table 4 shows the results for this estimation, which differed from those of an OLS model without spatial behaviour.

Table 4. Ordinary least square (OLS) and spatial autoregressive model (SAR) estimations. Dependent variable economic value (EV)⁽¹⁾.

The first two columns in Table 4 show the OLS estimation for firms’ economic values (EVs) that includes firms’ specific characteristics. We obtained a positive and significant sign for the explanatory variables, as expected according to the previous literature. Regarding the spatial behaviour of this model, we computed the LM tests. The LM-LAG test was positive and significant, thus revealing the existence of a spatial lag structure in the model, whereas the LM-ERR was not significant. Thus, the specification (9) was transformed into an SAR model, as in (10), where the spatial weight matrix (WL) was a row standardized weight matrix that is based on the s closer neighbours, and s = 11 (according to the results we obtained in the previous section).

The third column in Table 4 shows the estimation results of the SAR specification. We obtained a spatial lag parameter that was positive and significant (ρ=0.1914, p=0.007)). Thus, from the coefficients of the SAR model, we could estimate the value of a company without temporal information by combining the spatial and firm information. In particular, for a company i, we applied the following equation (11) to obtain the spatial-firm economic value (SFEV).

Comparing economic values

The average value for the absolute deviations bet­ween the SFEV and the EV computed by applying DCF for the fruit companies in the sample was SFEV-EV = 0.00075, which was lower than the absolute difference calculated as SEV-EV = 0.0804. Thus, we obtained a better approach when both the spatial and firm characteristics were considered in estimating the EV of a company without an extensive amount of temporal information. Specifically, we found that all variables considered have significant effects on firms’ valuations. Sales growth and SIZE were significant at 5%, whereas indebtedness, profitability and age are significant at 10%.