Material and methodsTop

Non-listed agri-firms’ valuation

The value for each firm of the sample was estimated as the Enterprise Value (EV). This value does not consider firms’ financial position but it was focused on the cash flows generated by operating activities. Our premise was that geography may influence on the input-output linkages in agrarian firms altering the capacity of these companies to generate cash flows. In order to estimate the EV, we applied the DCF model. This was one of the most commonly used methods to calculate firm’s value (Verginis & Taylor, 2004; Rojo & García, 2006; Dönbak & Ukav, 2016). DCF procedure discounts the free cash flows (FCF) that the firm will create in the future to present value by using an appropriate discount rate referred to as Weighted Average Cost of Capital (WACC). However, we found different specifications from this model in order to face particular characteristics of non-listed firms. In the present study, we applied Rojo & García (2005, 2006)’s proposal to estimate the discount rate for the case of non-listed companies. The difference between Rojo & García (2005, 2006)’s approach and that commonly used based on the Capital Asset Pricing Model (CAPM) is the addition of a specific risk premium in order to take into account the higher risk faced by non-listed companies when compared to their listed counterparts. Specifically, Rojo & García (2005, 2006) compute the expected return of equity (ke) for the case of non-listed companies by adding three components: the risk free rate (Rf) , the market risk premium (Pm) and a specific risk Pe (see [1]).

Rf and Pm were computed following the traditional literature (Damodaran, 2002<; Baginski & Wahlen, 2003) while Pe was calculated based on the concept of total beta (Damodaran, 2002) as shown in [2].

where the coefficient ßi is computed as the ratio of the standard deviation of financial profitability of the firm i after interest and taxes to the standard deviation of market return.

Once ke was computed, we could estimate the WACC (k) by applying the following expression:

where kd is the cost of debt, E represents equity, D is financial debt and t is the effective tax rate.

The spatial econometric model

We part from the following spatial econometric model [4] (Anselin, 1988; Le Sage & Pace, 2010):

where y is a (N×1) vector containing the valuations for each non-listed agrarian firm i in our sample, with i=1,…,N; X is a (N×(r+1)) matrix containing a constant term and r explanatory variables. In our case, the explanatory variables are representative of the distance between each company i and a strategic point that favours accessibility between the company and other economic agents. WL and WE are (N×N) spatial weight matrices that define, with values different from zero, the interconnections among companies; u is a (N×1) vector of the spatially correlated residuals; e is a (N×1) vector of normally distributed errors with mean zero and variance s2; ? is the spatial lag coefficient reflecting the importance of spatial autocorrelation in the valuation of non-listed Spanish companies with 0<|?|<1. If this coeficient was significant, this indicates that the analysed firms’ valuations depend not only on the internal firms’ characteristics but also on their vicinity firms’ valuation. ß is a (r +1) ×1 vector containing the regression coefficients for the explanatory variables, and ? is a coefficient reflecting the spatial autocorrelation of the residuals ui. The difference between previous spatial structures (in the dependent variable (WLy) vs in the error term (WEu)) was explained by the source of interdependence among companies’ valuation. In the first case, the spatial effect was caused by the structural character of firms’ valuation variable. If this structure was significant, then we can conclude that the particular characteristics of a company influence the valuation of companies in their vicinity. In the second case, spatial interactions in the error term are explained by the omission of relevant variables into the model that generates this result.

Previous model [4] was estimated applying maximum likelihood (ML) (Elhorst, 2010). The ML estimation is the most commonly used method based on the maximization of the log-likelihood function. The significance of the spatial structure ((WLy) vs (WEu)) can be determined by computing the Lagrange Multipliers (LM) tests and their robust versions for the POOL-OLS estimation: LM-LAG (LM-LE the robust version) and LM-ERR (LM-EL the robust version) (Anselin, 1988; Anselin et al., 1996). Both tests have as null hypotheses the absence of spatial autocorrelation and as alternative hypotheses the existence of a spatial autoregressive structure in the dependent variable for the LM-LAG test and a spatial dependence structure in the error term for the LM-ERR test. Following the methodology of Florax & Former (1992), from the particular to the general, we compared the values of both tests (LM-LAG and LM-ERR) and their robust versions. When representative tests of one spatial structure were significant but the others were not, then we selected the significant spatial structure according to them. For example, if we got a significant value for the LM-LAG and the LM-LE and non-significant values for the others, then we selected a model that only contains spatial autoregressive structure in the dependent variable (WLy). This model is known as the Spatial Lag Model (SLM), whereas the model with only spatial autocorrelation in the error term is known as the Spatial Error Model (SEM). However, when we obtained significant values in both spatial structures, then we estimated a spatial model as [4] known as the Spatial Autocorrelation Model (SAC).

In this study, we did not differentiate between the spatial weight matrices WL and WE. From a theoretical perspective, the SAC model was identified when there were additional explicative variables apart from the spatial effects (Le Sage & Pace, 2010). Therefore, it was not necessary to apply different weight matrices. From this premise, empirical studies assume that both matrices are equal (Kelejian & Prucha, 2010). The idea behind this assumption was that the weight matrix describes the space in which you are working and the spatial variables, that are the spatial interaction mechanisms associated to each variable in the explanatory part of the model or in the error term, adapt to this space but the space does not adapt to the variable. For the common spatial neighbourhood matrix W, we considered different standardized alternatives based on the q nearest neighbours. For example, if we consider the three nearest companies to each company i (q=3), then we are assuming an interconnection structure shown in Fig. 1 where each company, represented by a circle, has its three nearest companies as neighbours (Fig. 1A). In Fig. 1A, grey colour circles represent two different companies, and the continuous lines from each of them link these companies with their neighbours according to this criterion. If we consider a connectivity criterion based on the five nearest companies to each company i (q=5), then we have a connection structure as shown in Fig. 1B. In this case, grey colour circles also represent the companies to be considered as examples, and the continuous line connects each of them with their neighbours according to this criterion.

Figure 1. Example of q-nearest neighbors.

Based on previous q neighbour criterion, we defined the binary row standardized weight matrix W in which elements wij value one if the company i and j are neighbours and zero otherwise.

Empirical application

We part from the DCF valuation method for non-listed companies to show an empirical application on a sample of Spanish agrarian companies with the aim of testing whether the geographical proximity among peer companies and/or from these companies to certain strategic points influences the valuation of these firms in the agrarian sector.

Database

The information to develop this empirical application was obtained from SABI (Iberian Balance Analysis System) database. This database provides a wide range of information about the different business dimensions of Spanish firms. We chose Spanish agrarian companies2 following the criterion established in the National Classification of Economics Activities (NACE, 2007). In order to avoid heterogeneity in the sample, we selected companies located in the province of Murcia in Spain (Fig. 2).

Figure 2. Firms’ spatial distribution. Provincial map.

We selected this territory because of the important weight of the agrarian sector on the global production of this region (INE, 2013). Once we obtained all of the information, we removed the observations with missing information to the calculation of the EV and those having anomalies in their financial statements, e.g., negative values in their sales or assets that distorted the behaviour of the firms. Companies with negative values in their cash flows were also excluded from the analysis. Furthermore, to reduce the effect of outliers in our sample, we dropped extreme values in all of the variables that were not included in the ± 3 interquartile range. Our sample contained information for 548 non listed-agrarian companies over the period 2010-2014.

In addition to firms’ financial information, SABI database also provides the location of each company through the geographical coordinates of each. Finally, we also hand-collected the geographical location of some strategic points (such as airports, train stations, and city centres) in Murcia using Google-Maps.

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Variables

Firms’ values

In order to estimate the EV, the DCF model was disaggregated into two stages. A first stage focused on the current value of future cash flows and a second stage which calculates the residual value (RV) (or continuing value) (Jennergren, 2008; Ribal et al., 2010). The EV for each company for the year 2014 was calculated as [5].

where t represents every year in the period from 2015 to 2019 and l the number of years of this period (l=5). FCF was calculated for each company in t using the standard formula [6]

where EBIT is the earning before interests and taxes; D&A, depreciation and amortization; Imp, impairments; ?WC, working capital changes; and I, investments in non-current assets. Depreciation and amortization as well as impairments related to non-current assets are added to EBIT (earnings before interest and taxes) in so far as they do not involve a cash outlay while working capital variation was considered in order to take into account those sales and purchases on credit recognized in EBIT that have not yet generated a cash movement. Therefore, in order to estimate future FCF for the next five years (2015-2019) we had to assume the evolution of the main components of FCF. In this regard, we fitted a linear regression based on data on each company's historical sales and extrapolated future sales based on the linear model fitted (Alekneviciene et al., 2013). Once future sales were estimated, we projected the rest of the components of FCF by applying the mean of the annual past values of the proportion (ratio) that each FCF component represents with respect to historical sales (Alekneviciene et al., 2012).

We got the discount rate (WACC) applying the previous expression [3] for non-listed companies. The cost of debt (kd) was calculated as the ratio of interest expenses to the financial debt of the company. As usual when implementing DCF, the risk free rate (Rf ) was proxied by the 10-year government bond interest rates. We obtained this information from the webpage www.datosmacro.com, which provides financial sector information about different Spanish markets. The market risk premium (Pm) was considered to be the average historical differential between market returns and risk-free rates during the last years. We got this information from Damodaran’s webpage3 which provides market risk premiums by industries and countries. The specific business risk (Pe ) was computed according to expression [2] where financial profitability of the firm i after interest and taxes (i.e., ROE) was obtained from firms’ accounting information and market return from Damodaran's webpage. Finally, we determined the RV by applying the Gordon model that assumes that FCF will grow at a constant rate (g) after the estimation period. Analytically:

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

Explanatory variables

Explanatory variables in this analysis were representative of the distance between each company in the sample and a strategic point. In order to determine the geographical distance between each company and these strategic points, we built an algorithm in R software. Following previous literature, we considered these strategic points: a) industrial parks, b) shopping centres, c) road nodes, d) airports, e) train stations, f) technological centres and g) city centres. Apart from these variables, we also included control variables to take into account the characteristics of each company. In this regard, we defined the age and the size of the company, establishing different categories for each variable. Following Bergel & Udell’s (1998) study, we defined four groups of companies according to their ages: infant (0 to 2 years), adolescent (3 to 4 years), middle-aged (5 to 24 years) and old (more than 25 years). The variable size was based on the number of employees. From this information, we followed the Commission Recommendation 2003/361/EC (OJEU, 2003) to determine different groups. Micro was composed of companies with fewer than 10 workers. Small was defined as the set of companies with between 11 and 50 employees. Medium refers to companies with 50 to 250 employees. Finally, Large indicates the group of companies with more than 250 employees. Small and young firms have specific characteristics, such as informational asymmetries, that make them riskier and with a higher probability of bankruptcy (Dhawan, 2001; Chava & Jarrow, 2004; Vassalou & Xing, 2004; Chen, 2010). Therefore, we expected that these companies would present lower valuations. In this sense, the high bankrupt’s risk was reflected in the DCF model with a higher discount rate (WACC) influencing negatively on firms’ valuations.

Table 1. Moran’s I test considering different weight matrix based on q nearest neighbors.

Table 2. Estimations of the agrarian valuation on locational variables