When companies are aware of their financial results, they take into account their peers’ financial practices as reference values. Graham and Harvey (2001) examine this behaviour through a comprehensive corporate survey. They show that firms are concerned about their peers’ financial behaviours. In particular, their results indicate that peers’ debt average value impact by 23,40% on how the company choose the appropriate amount of debt. This percentage turns to 22.93% when the company considers issuing common stock. In a more recent study, Leary and Roberts (2014) show that peer actions play an important role in determining firms’ financial decisions. In fact, this effect is more important for capital structure determination than mostly of the previously identified determinants. This is explained by the indirect peer effect that amplify the impact of changes in exogenous factors on leverage by over 70%. In this context, we state that geographical proximity between companies plays a significant role strengthening this peer effect. In this sense, space intensify interconnections between companies facilitating the mimicking of financial practices between geographically close companies (Maté-Sánchez-Val et al., 2017).

Thus, we argue that financial information of geographically close peers may be a useful source of information to approach companies’ valuation. This proposal has far-reaching implications on firms’ valuation processes when temporal information is not available. In particular, this proposal is ideal for reduced size companies that present simplified financial statements (Damodaran, 2009; Plenborg and Pimentel, 2016; Vidal and Sanchis, 2017) and could be an useful tool to solve the problem of the estimation of news companies’ economic values (Miloud et al., 2012; Dusatkova and Zinecker, 2016). Financial literature presents several procedures to compute valuations for listed companies, but these methods have limitations for non-listed reduced-size companies. In order to overcome this barrier, further valuation procedures consider the specific risks of these companies (Marquez-Perez et al., 2017). A well-known procedure is presented in the studies of Rojo and García (2005 and 2006). These authors present a three-component proposal to determine the small companies’ valuations. This method is based on the widely used Discounted Cash Flow (DCF) model by adding a specific risk premium for small companies. Nevertheless, to apply this procedure, temporal information is required to estimate future data from firms’ financial statements. But, one of the main limitations of applying traditional methods is the absence or unrepresentativeness of firms’ historical data (Damodaran, 2009). In order to overcome this limitation, financial information of geographically close peers could play a relevant role to estimate reduced size firms’ valuations. In this sense, in a recent study, Occhino and Mate (2017) identify the existence of spatial concentration areas of small companies with similar valuations. They further examine the causal relationship finding that average valuations of geographically close peer companies have a significant effect on firms’ values.

Thus, given the relevance of peer effect on firms’ valuations when geographically close environments are examined, we proposed a method to estimate the valuations of those companies with scarce temporal information by including spatial data. The procedure starts by defining spatially comparable companies as those companies acting in the same sector and with similar characteristics and a geographically close distance between them. The suggested classification is derived from a known underlying theoretical foundation (e.g. profit maximization, economies of scale) following financial literature on valuation methods of multiples. Then, we identified spatial clusters of companies whose valuations are interconnected and proposed a spatial valuation approach based on firms’ internal characteristics and spatially comparable’ valuations. To make our point, we presented a study case on a sample of industrial small and medium size (SME) companies located in Madrid, Spain. We further estimated differences from our spatial proposal and traditional methods with promising results.

We were able to find a spatial valuation approach taking into account that geographically close firms are financially linked between them. We believe that our approach offers a complementary perspective in the valuation methodology that may constitute a proper contribution for estimate the value of firms without available temporal information, as reduced size companies. Our main claim is that geographical proximities induce the existence of networks between companies causing a financial contagion effect and mimic actions which should be considered in the valuation process. This reasoning will be particularly exposed in the next section.

The rest of the paper is organized as follows; the Section 2 shows theoretical background. Section 3 gives basic definitions and formal concepts, and describes the procedure. In section 4 a case study for industrial SMEs is presented. We conclude and discuss several implications and limitations of our method in the last section.

Recent studies highlight social managers’ networks as a significant element in their financial decisions (Shue, 2013). In this sense, empirical analysis find that available information about peers is considered when financial practices-such as capital structure and/or capital budgeting- are adopted. This is known as peer effect. Peer effect refers to a situation where a company reacts in response to its peers actions (Maquieira et al., 2012). This effect is different from common or correlated effects derived from the fact that companies present similar characteristics or are located in common environments (Grennan, 2017). Financial literature identifies the peer effect from different theoretical perspectives (Park et al., 2017). From the herd behaviour model, the peer effect is caused by the fact that companies mimic other companies independently from their available internal information. From the strategic intentions model, companies consider peer effect to adopt strategies affecting the financial results of other companies in the market (Rajan, 1994). Another theory related to peer effects comes from the learning behavior model. This model states that firms use information as an instrument for adopting rational decisions (Chevalier and Scharfstein, 1996). For example, financial literature of trade off indicates that there is an optimal capital structure. Thus, managers should adjust their financial variables towards this target. Nevertheless, a rational decision maker would value financial practices of their peers to make their own decisions instead of determining the optimal capital structure, which would be more complicated (Bikhchandani et al., 1992). Finally, behavioral preferences model indicates that managers act following irrational anticipations. Thus, peer effect could be used to identify anticipations of future financial situations and therefore, would be imitated (Malmendier and Tate, 2005).

Financial studies tend to omit previous theoretical arguments about the significant role of peer effects (Zaighum, 2019). Nevertheless, Leary and Roberts (2014) in a recent study, considers peers’ interactions finding a positive correlation between the increase in the peers’ average leverage and the increase in a firm’s leverage value. Francis et al. (2016) propose an international analysis, concluding that companies in both developed and developing countries, decide their leverage values based on their peers’ information. Grennan (2017) finds that managers take into consideration peers dividend policies when deciding their own firms’ dividend policies. Finally, Fairhurst and Nam (2018) show that the U.S. firms that have weak external corporate governance are more prone to mimic their peers’ capital structure choices.

In this context, recent studies states that the geographical proximity between companies play a significant effect strengthening the peer effect in firms’ financial decisions. In this sense, Maté et al. (2012) identify a spatial concentration area constituted by companies with similar values for their financial ratios. They propose a model to estimate the causal relationship of peers financial ratios on firms’ financial ratios with significant results. They conclude that the impact is more intense when the distance between geographical companies is reduced. In addition, reduced size companies are more affected by this effect. Mate et al. (2017) provide a similar analysis with a sample of industrial reduced size companies corroborating that space plays a relevant role on peer effects intensifying interactions in financial decisions between geographically close companies. The theoretical explanation of the accelerator effect of space is based on the economic arguments of transportation costs and external economies (Fujita and Thisse, 1996). On the one hand, the theory is based on the hypothesis that geographically close companies have easy access to external resources minimizing transportation costs. Therefore, geographically close companies tend to establish commercial relationships which at the end will provide additional information about the financial practices of their geographically close peers. In this sense, Selan and Kalatzis’s study (2017) indicate that there is a positive and statistically significant spatial dependence between stock return from peers companies. Occhino and Mate (2019) provide evidence about the significant role of geographical proximity when financial results from commercial interrelationships are examined. On the other hand, the external economies theory states that companies’ location triggers different forms of interaction between firms and between firms and their environment (Marshall, 1920). From this perspective, there are knowledge spillovers cause a flow of information between agents working in the same geographical area. Geographical proximity facilitates the formation and transmission of social capital, enhancing trust and the ability to share vital information (Karlsson et al., 2015). Managers working in the same environment normally have the opportunity to build face-to-face relationships, exchange ideas and learn from one anothers’ experience. As a result, positive network externalities will ensue and companies will be able to learn from the failure and success of other firms sooner than they would if no direct contact between was possible (Maskell, 2001).

Our spatial valuation proposal is based on the steps showed in the following Figure 1.

In order to test our proposal, we undertook an empirical application with a sample composed by industrial reduced size firms located in Madrid, Spain.

The aim of this study were to propose a method to estimate firms’ economic valuations that have short term temporal histories of available data or for reduced size companies that present simplified financial statements. In contrast with previous studies, we considered both firms’ internal characteristics and geographical information. This procedure is based on the financial hypothesis that financial practices between reduced size peer companies tend to present certain similarities. We tested our proposal finding good results. In this sense, we tested that companies in the analysed sectors tend to have similar values when grouped in small areas; consequently, it is possible to use the EVs of peer firms as a reference in order to value a company without possessing all the necessary information. Based on previous literature, we combine external informtion with firm’s intrinsic characteristics (age, size and sales growth). This spatial proposal is based on the vast literature on multiple methods, which recommends extrapolating information using a group of similar companies as a reference (Eberhart, 2001). It is based on the implicit assumption that identical firms should be have identical value. For SMEs, in order to obtain a more precise estimation, it is advisable to consider firms in the same sector and same region given that small firms are heavily dependent on the economic situation in which they operate (Schreiner, 2009). Our test provided a positive result, and want give an ulterior input on the analysis of the key value drivers for SMEs valuations. The aim of the study is to open up a new field for further investigation. Using this spatial perspective, would be possible to obtain valuations for new SMEs characterized by the lack of available data. Our results provided good adjustments for those subsamples composed by a reduce number of companies whereas the adjustmet was weaker for those subsample with a larger number of companies. This result could be motivated by the higher firms’ herterogeneity for this group. Thus, further research could analyse this aspect in order to solve this particular issue. Moreover, the present study is first step so need to be tested in other scenarios and subsectors.

Many scientists consider the Discounted Cash Flow (DCF) valuation as the most accurate valuation method (Fernández, 2013; French, 2013; Dönbak and Ukav, 2016). Based on DCF, the Economic Value (EV) is computed discounting the future free cash flows (FFCF) that the firm will create in the subsequent years using a discount rate (k). k is usually assumed to be the weight average cost of capital (WACC). Thus, the EV for each company for the year t is calculated as in (A.1):

(A.1) \displaystyle{EV_{t}=\sum\limits_{i=1+t}^{l}{\frac{FFCF}{(1+k)^t}+\frac{RV}{(1+k)^l}}}

This is a two-step method. In the first step the earning of the next five years (Damodaran, 2002) have to be estimated and discounted at the valuation year. In the second step a Residual Value have to be computed. This happen because a firm have an infinite life and forecast valuations should be calculated for the same period. It is obviously difficult and therefore, we need to limit the period of valuation by targeting a particular year that is why Residual Value, which is the last value in the last year were targeted. This value is usually a very important part of the total value; thus, its estimation is a key activity in the valuation process (Esteban, 2018). Residual Value was determined applying the Gordon model that assumes that FCF will grow at a constant rate (g) after the estimation period (A.2) (Copeland et al., 2010):

(A.2) \displaystyle{RV=FCF_{t+1}\frac{(1+g)}{(k-g)}}

This work estimated (A.2) after the projection period there will be a 1.5% of growth. In order to estimate the free cash flow (FCF) (A.3) we used the one most widely formula used in the business environment (Damodaran, 2007; Fernandez, 2013).

(A.3) FCF=EBIT(1-t)+D\&A+Imp+\Delta WC-I

Where EBIT is the earnings before interests and taxes, D&A represents the depreciation and amortization, Imp represents impairments, ∆WC evaluates the changes in working capital, and I measures the investments in non-current assets. In order to estimate FFCF for the next five years (2017-2022) we had to assume the evolution of the main components of FCF. In this regard, we followed the traditional literature (Alekneviciene et al., 2013) fitting a linear regression based on data on each company's historical sales and extrapolating future sales based on the linear model fitted. Once future sales were estimated, we projected the rest of the components of FCF assuming the mean of the ratios among each FCF component and the historical sales remain constant (Gentry & Reilly, 2007). The FCF are discounted by using the WACC, (A.4).

(A.4) \displaystyle{WACC=K_e\frac{E}{(E+D)}+K_{d}(1-t)\frac{D}{(E+D)}}

The cost of debt is calculated as an approximation using the financial expenses and the current debt of the company, (A.5).

(A.5) \displaystyle{K_d=\frac{FE}{D}}

The capital structure is taken from the company’s books given that many studies use the book value of debt and equity in order to estimate the capital structure in a DCF method (Woolley; 2009).

One of the main problems in business valuation when we apply the DCF Model is how to include risk from the uncertainty associated with future cash flows (CFs) (Cañadas and Rojo; 2011). Usually risk is included in the discount rate (k_e ) and represent the risk assumed by the company. This method is known as ‘‘discount rate method with risk’’ or ‘‘traditional approach.’’ According to Bruner et al. (1998) and Graham and Harvey (2001), the most commonly used method in practice to estimate the risk for an investor is the CAPM (Sharpe 1964). Following the traditional literature, discount rate of a firm (k_e ) is the sum of the risk-free rate (R_f ) and the risk premium (P_M ) given to the difference between the R_f and the sectorial premium rate (R_m ) (A.6).

(A.6) k_e=R_f+\beta_i (R_m-R_f)

The individual beta of each company is obtained by unlevering each food firm beta using the Modigliani and Miller´s (1958) beta formula (Vidal and Sanchis; 2017). The unlevered beta, in the valuation of privately-held firms, is usually estimate using the formula, Eq. (A.7) (Petersen et al.; 2006).

(A.7) \displaystyle{\beta_u=\frac{\beta_t}{[1+(1-t)\frac{D}{E}]}}

Then, industry beta is levered by using the capital structure of the individual company, following Eq. (A.8).

(A.8) \displaystyle{\beta_l=[1+(1-t)\frac{D}{E}] \beta_u}

It is possible to get the necessary information from Damodaran’s webpage which provides market risk premiums by industries and countries. However, we found different specifications from this model in order to face particular characteristics of non-listed firms. In this sense, an interesting specification is proposed by Rojo and García (2005, 2006). The difference between Rojo and 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 (Occhino and Maté, 2017). Rojo and García (2005, 2006) compute the k_e adding a specific risk P_e . The argumentation to this proposal is that the valuation of privately-held firms often involves investors who are not well-diversified. Thus, an investor that cannot diversify his investment need to have a higher premium risk that reflect also the specific risk of the firm (Rojo, 2013).

(A.9) k_e=R_f+P_M+P_e

Rojo-Ramírez et al. (2011) demonstrated that P_e can be calculated how showed in eq (A.10):

(A.10) \displaystyle{P_e= P_M \frac{\sigma_e}{\sigma_M}}

Where σ_e is the standard deviation of the profitability of the company and σ_M is the standard deviation of the profitability of market. 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.

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¹ See Annex for further details about the application of these methodologies.

² The RMSE is computed as the square root of the quadratic mean of the difference between predicted and observed values.