*Technical University of Cartagena (UPCT), Dept. Accounting and Finance, Calle Real 3, 30201 Cartagena (Murcia). Spain.*

*Technical University of Cartagena (UPCT), Dept. Accounting and Finance, Calle Real 3, 30201 Cartagena (Murcia). Spain.*

The Discounted Cash Flow (DCF) model, similar to other frm valuation models, uses temporal information for a frm to forecast future results. However, the lack of temporal information for many companies hinders the application of the DCF model. To overcome this limitation, we proposed an approach based on the spatial information of the analysed companies. In particular, to get frms' valuation our approach combined both data from companies that are geographically proximal to the analysed company and data from the analysed company. Based on this approach, we provided an empirical example to demonstrate that the economic value computed with our proposal, the Spatial-Firm Economic Value, was consistent with the traditional economic value after application of the DCF model. In particular, we found a minimal difference in terms of absolute deviations between our proposal and the frm's valuation applying traditional valuation techniques. Thus, this study demonstrated the relevance of considering the spatial dimension as an additional source of information to determine frms' value in the Fruit subsector when there is not available temporal information to apply traditional valuation methods.

The important weight of Small and Medium Enterprises (SMEs) in current productive systems and globalization has increased demand for SME valuation. The limitations associated with the reduced scale of these companies can be overcome by mergers and acquisitions, which depend on firms' valuations. Several procedures can be applied to obtain firm valuations for large companies acting in stock markets, but these techniques are limited for reduced-size companies. In fact, without access to capital markets, SME valuation methods have focused on the specific risks of these firms (Marquez-Perez
^{1}

To illustrate our proposal, we developed an empirical application on a sample of 280 companies in the fruit subsector located in Murcia, Spain, for which there is temporal available information. In this way, we compared the results applying the traditional valuation models with our proposal. Based on this sample, we applied spatial econometric techniques to determine the set of

Rojo-Ramírez (2014) for further details.

Let us suppose that we need the valuation of a company without available temporal information. To overcome this limitation, we proposed an approach based on geographical information and the steps presented in the

Reduced-size companies have more opacity in their information (

where

In this equation, EBIT is the earnings before interests and taxes, D&A represents the depreciation and amortization,
^{2}

The discount rate
_{e}) by adding a three component method based on: the risk-free rate (R
_{f}), the market risk premium (P
_{m}) and a specific risk premium (P
_{e}) (

R
_{f} and P
_{m} are computed according to the traditional literature (
_{e} is calculated as shown in (4):

where β
_{i} is computed as the ratio of the standard deviation of financial profitability of firm i after interest and taxes to the standard deviation of market returns. With (7) and (8), we can estimate WACC (k) by using (5):

where k
_{d} is the costs of debt, E is the equity of the company, D is its financial debt, and τ is the effective tax rate.

Thus, the previous method is applicable in those companies with available temporal information. In this sense, the estimation of FCF will require a forecast analysis for which data along a number of years are involved.

The first step of our proposal is to identify spatially comparable companies. This definition is based on the financial literature on evaluation methods of multiples, which suggests that it is possible to extrapolate information using a group of similar companies as a reference. This peer group should consist of at least two and up to a maximum of ten comparable companies (

Thus, considering the relevance of geography for SMEs, we defined spatially

where
_{i} and
_{j} represent the value of the variable
_{ij} represents the (
_{ij} take a value of 1 if companies
_{0} is the sum of all elements of the matrix

Once the

where

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 (
^{3})

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.

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 (
_{d}), calculated as the ratio of interest expenses to the financial debt of the company. The cost of equity (k
_{e}) is computed from (3), where the risk-free rate (R
_{f}) is represented by the 10-year government bond interest rates
^{4}_{m}) 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 webpage
^{5}_{e}) was computed by

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

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 (

We found

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

In this equation,
_{L} and
_{E} were (280×280) spatial contiguity matrices that define the connections between the companies in the sample;
^{2}. 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
_{L}
_{E}

The first two columns in _{L}) was a row standardized weight matrix that is based on the

The third column in

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%.

The aims of this study were to test and propose a method to estimate the EV for firms that have short temporal histories of available data or for which it is difficult to obtain information. In contrast to previous studies, we considered financial and economic variables as well as environmental variables. We observed the best results when we considered both spatial and firm characteristics to estimate the EV of a company without an extensive amount of temporal information. In this sense, we observed that companies in the fruit subsector with similar values tend to be grouped in the territory; consequently, it is possible to use the EVs of comparable firms as a reference. To obtain the best estimation, it is necessary to adjust this value for a coefficient that takes into consideration the firm's intrinsic characteristics (age, size, indebtedness, profitability and sales growth). Our results are justified by the previous literature on multiple methods, which suggests extrapolating information using a group of similar companies as a reference (

Our study presented a proposal for SMEs' valuation and demonstrated the importance of considering the spatial dimension as an additional source of information in the Fruit subsector. This study opens up a new field for further research. Using this spatial perspective, it is possible to obtain valuations for small and medium-sized companies and/or companies without available information complementing missing financial data. Nevertheless, our study has limitations that provide opportunities for further exploration. Our sample is composed by companies in the fruit subsector thus future research in this area should consider other scenarios and different subsectors to overcome this limitation.

Rojo-Ramírez (2014) for further details.

It is common the use of the Earnings Before Interest and Taxes (EBIT) of the frm as starting point to calculate the FCF but, in general terms, revenue
growth tends to be more persistent and predictable than earnings growth because accounting choices have a far smaller e?ect on revenues than they do
on earnings (see Stowe

We obtain this information from