Covariance matrix adaptation evolution strategy based optical phase control

In this letter, an investigation of the use of a covariance matrix adapta- tion evolution strategy (CMA-ES) algorithm is conducted as the phase-locking method for multi-channel coherent beam combining (CBC) for the ﬁrst time. A comprehensive numerical analysis is carried out on the operational performances of the CMA-ES based phase-locking al- gorithm implemented into 7- and 19-channel CBC systems in a ﬁlled-aperture format. Through numerical simulations it can be veriﬁed that the CMA-ES algorithm can readily lead to over 0.90 of normalised beam combining efﬁciency with appropriate algorithm parameter sets, which can also be optimised by a combinatorial study. The proposed CMA-ES based phase-locking algorithm is a feasible option for novel phase-locking technique for a CBC system particularly when the local extremum issue becomes severe such as in CBC under turbulent atmo- spheric conditions.

Introduction:
The scaling of the continuous-wave near-single-mode laser power beyond ∼10 kW is not straightforward at all because of the non-linear and thermal effects such as Brillouin/Raman scattering, self-focusing, transverse mode instability etc. [1,2]. While a number of strategies have been proposed to mitigate such effects, there is indeed a limit for the maximum power that a single strand of fibre laser can handle [1]. Consequently, various beam-combining techniques have emerged to overcome the single-fibre's limitation, which particularly include the spectral beam combining (SBC) and coherent beam combining (CBC) techniques [3]. In fact, a lot of experimental demonstrations have shown that beam combining techniques are a viable route towards the next level high-power laser system [4,5].
In particular, the CBC technique has earned a lot of attention by virtue of its high-performance characteristics when realised appropriately, e.g. excellent beam quality, high on-axis intensity, high-adaptability for wavefront correction etc. [3]. In this case, the phase locking of each channel beam of the CBC system is the primary key to success, for which the following three well-known phase control algorithms are mainly adopted to control each channel beam's phase, optical homodyne detection (OHD), locking of optical coherence via single-detector electronicfrequency tagging (LOCSET), and stochastic parallel gradient descent (SPGD) [5,6]. The OHD obtains the phase information of channel beams by comparing each channel's phase with that of a fixed reference channel, thereby requiring as many detectors as the channel beams. By contrast, both LOCSET and SPGD operate with a single detector. The LOCSET is implemented by tagging a different frequency on each channel and extracts the corresponding phase information from the beating signal with other channels. It can control the phase with high accuracy; however, as the number of channels increases, the number of tagging frequencies and the calculation time required for obtaining the whole phase information increase at the same time. On the other hand, the SPGDbased phase-locking is performed through an iterative intensity maximisation process by applying a set of arbitrary phase perturbations to the individual channels [5,7]. Since the phase-locking is implemented without extracting the phase information of the individual channels, it offers simple, fast, and straightforward features. However, given that the SPGD is a derivative-based algorithm, it is susceptible to fall into local extrema so that additional methodological measures should be put together in order to keep away from such undesirable situations [8].
We here propose a covariance matrix adaptation evolution strategy (CMA-ES) based derivative-free phase-locking technique, which can be implemented with a single detector in place of the SPGD technique. Through numerical analyses of the phase-locking of conceptual CBC systems of 7-and 19-channel beams, we substantiate the performances of the CMA-ES based phase-locking algorithm applicable for CBC systems, to the best of our knowledge, for the first time.
Basic principle of CMA-ES based phase-locking: Like SPGD based optimisation algorithms [7], CMA-ES based phase-locking can be obtained by means of the optimisation of the peak or overall intensity of the combined beam while iteratively applying sets of phase perturbations onto the multi-channel input beams. However, unlike SPGD based algorithms which determine the phase perturbations for the next iteration step by taking the derivatives of the perturbations of the preceding steps, CMA-ES algorithms determine them by referring to a statistical distribution function (the covariance matrix) which is iteratively updated by some "selected" phase perturbations which have shown the higher probabilities in the preceding steps [9]. In fact, such derivative-free optimisation procedures are very advantageous in resolving the local extremum issues which the SPGD based algorithms often encounter. Thus, CMA-ES algorithms have been receiving high research attention in numerous fields in recent years [10].
In the case of CBC, the local intensity fluctuation grows substantially as the number of channel beams to be combined increases, because of the multiple interference effect [8]. Consequently, we note that the local extremum issues will also grow accordingly as far as CBC systems rely on derivative-based algorithms. We here investigate CMA-ES based phase-locking algorithm implemented onto CBC.
Let us suppose that there is an N-channel CBC system, the N-channel beams of which are phase-controlled based on the CMA-ES algorithm. The initial phase of each channel is unknown, being randomly determined in between 0 to 2π rad. Thus, the CMS-ES algorithm should find a compensating phase for each channel beam such that all the channel beams eventually result in an in-phase combined state at the target plane. The general procedure is based on the five steps as follows.
(i) Apply I sets of phases (samples) sequentially onto each channel beam.
(ii) Select top J (J < I) sets of phases (elite samples) which give the highest combined beam intensities. (iii) Calculate the covariance matrix and the mean value of the selected J sets of phases from (ii). (iv) Update new I sets of phases which have the probability distribution represented by the covariance matrix calculated in (iii), and apply them onto each channel beam. (v) Iterate the above steps until an optimal set is found.
Depending on the sizes of I and J, the optimisation performances, e.g. accuracy, time elapsed, may vary. However, it is relatively easy to make them suitable for optimisation of the given situation, because they are just numbers indicating the samples and elite samples used, unlike many other algorithms which normally rely on quite complex and sophisticated parameters [11].
Simulation results and discussion: Given that a hexagonal array of channel beams are generally applied to a CBC system, we consider two different cases of CMA-ES based phase-locking for 7-and 19-channel CBC systems.
Implementation of the CBC technique can be made in two ways: One is the tiled-aperture configuration and the other is the filled-aperture configuration [3]. In Figure 1, we illustrate conceptual schematics for the filled-aperture configuration, which can be realised based on a free-space diffractive optical element (DOE) or an all-fiberised combiner (AFC), for example. In particular, the filled-aperture configuration offers a simple and compact arrangement for CBC, which hints at a best conceptual Thus, in the following simulations, we assume that the N-channel CBC system is based on the filled-aperture configuration and that each channel is based on an ideal Gaussian mode with a randomly determined arbitrary initial phase. We also assume that the DOE or AFC's efficiency is 100% and that there are no other additional loss or distortion mechanisms involved with it. We define the beam combining efficiency (BCE) as the ratio of the peak intensity of the combined beam obtained by the CMS-ES algorithm with respect to the theoretical maximum of the peak intensity of the combined beam in the ideal condition. It is noted that the theoretical maximum is calculated based on the assumption that all the N-channel beams are absolutely in phase at the target plane. We first perform beam combining simulations for various sets of algorithm parameters (i.e. # of samples, # of elite samples), based on which we determine the range of algorithm parameters for further investigation from the perspective of beam combining performance. We fix the total iteration number for the CMA-ES optimisation for a single trial to be 100, and repeat the trial 50 times with a renewed initial phase set.
Phase locking of 7-channel beams: We first applied the CMA-ES algorithm to the phase-locking of a 7-channel CBC system, trying various combinations of the algorithm parameters. In Figure 2, we show the simulation results on the peak intensity of the combined beam normalised by its theoretical maximum, i.e. the BCE, when we chose (10, 3), (10,5), and (15, 4) for the algorithm parameter set (# of samples, # of elite samples) throughout the iteration. For 10 samples, we note that with 3 elite samples, the BCE were widely spread, having the minimum BCE of ∼ 0.4. When we increased the elite sample number to 5, we could obtain significantly improved phase-locking performance as one can see that the higher BCEs acquired more counts. The overall average BCEs over the 50 trials for both cases were given by 0.89 and 0.95, respectively. Furthermore, for the algorithm parameter set of (15, 4), we obtained an even more significant enhancement in the phase-locking performance resulting in the overall average BCE of 0.98, which implies that increasing the number of samples is more effective in improving the performance of phase-locking than increasing the number of elite samples.

Phase locking of 19-channel beams:
We secondly applied the CMA-ES algorithm to the phase-locking of a 19-channel CBC system, also trying various combinations of the algorithm parameters. In Figure 3a, we show the simulation results on the phase locking of 19-channel beams with  the exact same algorithm parameter sets that were used in the case of 7channel beams as shown in Figure 2, i.e. (10,3) and (10,5). The results exhibit that the BCEs are much more widely spread than those for 7channel beams even with the same algorithm parameter sets. The overall average BCEs are reduced down to 0.77 and 0.89 for the cases of 3 and 5 elite samples, respectively. The reason for the degradation of the BCE in this case must be obvious that the CMA-ES algorithm should deal with even more channel phases for optimisation. In Figure 3b (a,b) for a 7-channel CBC system; (c,d) for a 19-channel CBD system parameter set, with which the overall BCEs for both cases were improved up to 0.89 and 0.97, respectively. This is quite a significant improvement although these cases required more elite samples in comparison with the cases of 7-channel beams.
Parameter optimisation: We have seen that the BCE can considerably vary with how we choose the algorithm parameters although the CMA-ES algorithm works effectively for finding optimised phase-locking conditions for both 7-and 19-channel CBC systems. We have thus carried out a combinatorial analysis of the optimisation of the algorithm parameter set itself. In Figures 4a and 4b, the simulation results on the mean value of the BCE and the corresponding standard deviation for a 7-channel CBC system under various parameter conditions are shown, respectively. One can see that the CMA-ES phase-locking algorithm can yield the BCE in excess of 0.90 as far as the number of samples is set equal to or greater than 10. In addition, one can see that at a fixed number of samples, increasing the number of elite samples invariably yields a smaller standard deviation of the BCE, i.e. it results in a more consistent phase-locking characteristic for every trial. It is noteworthy that increasing the number of samples does not necessarily lead to the improvement in the BCE, because the total iteration number is fixed to 100. While a large set of phases may have an advantage in obtaining various possible combined intensities, it may give rise to generating duplicated phase sets that may eventually result in similar combined intensities. This may, in turn, give rise to too broad a distribution of the next-step phase sets represented by the covariance matrix, so that the convergence to the optimal phase set can arguably be disturbed. Thus, we need to pay attention to the optimisation of the algorithm parameter set itself with care.
In Figures 4c and 4d, the simulation results on the mean value of the BCE and the corresponding standard deviation for a 19-channel CBC system under various parameter conditions are shown, respectively. Like the 7-channel CBC system, the CMA-ES phase-locking algorithm can yield the BCE in excess of 0.90 as far as the number of samples is set equal to or greater than 10. Also, one can see that increasing the number of elite samples leads to enhancement in the standard deviation of the BCE.
After all, in the case of the 7-channel CBC system, the best phaselocking performance obtained by the CMS-ES algorithm was given by the BCE of 0.98 and the standard deviation of 0.02 with the parameter set of (15, 5), (20, 4) or (25, 5). In the case of 19-channel CBC system, the best phase-locking performance was given by the BCE of 0.98 and the standard deviation of 0.02 with the parameter set of (20, 8) or (25, 7). We however note that the parameter set which yields the best performance in terms of the BCE and the corresponding standard deviation does not necessarily mean the best of all in that the CMA-ES phaselocking performance should also be justified in terms of a convergence time as well. In other words, given that the time elapsed for a single iteration the number of iterations for full convergence may vary depending on the choice of parameter set. Considering that the BCE in excess of 0.90 is acceptable for a CBC system as in the experimental studies previously reported [5,7], the algorithm parameter ranges of the number of samples between 15 and 20 and the number of elite samples between 5 and 7 should be of great interest.

Conclusion:
We have proposed a novel CMA-ES based phase-locking algorithm for a CBC system. With a comprehensive numerical investigation on 7-and 19-channel CBC systems, we have verified that the CMA-ES based phase-locking algorithm is a viable alternative to the existing phase-locking methods for CBC [9]. We have also analysed the mean BCE and the corresponding standard deviation through a combinatorial study on the algorithm parameters. In general, it is well known that a derivative-based optimisation algorithm like SPGD has severe drawbacks in situations when the derivative of the object function of optimisation is unreliable or hard to evaluate [12], for example, when the object function encounters numerous local extrema or drastic changes around them. Thus, a derivative-free optimisation algorithm is often looked for and implemented to overcome such drawbacks [12,13]. Given that the phase-fronts of laser beams can be distorted and fluctuated severely under the outdoor conditions for atmospheric turbulence [13], the objective function of optimisation for CBC can also suffer from such issues. In this light, the derivative-free CMA-ES algorithm can be a feasible, alternative phase-locking algorithm for CBC.


The Impact of Working Capital Management on Profitability: Evidence from Listed Companies in Sri Lankan Consumer Staples Sector.

This study aims to investigate the impact of Working Capital Management on Profitability with special reference to the Consumer Staples Sector firms in Sri Lanka. Further, this sector displayed a considerable growth potential in Sri Lanka. This study is adopted in a quantitative research approach. Data were drawn from a sample of 46 Consumer Staple Sector firms listed in the Colombo Stock Exchange (CSE) for a period of five years commencing from 2014/2015 to 2018/2019. To test the hypothesized relationships between the constructs, the panel data analysis is performed using STATA. The study found that the Inventory Conversion Period has an insignificant negative impact on Profitability. Receivables Collection Period negatively and significantly impact the Profitability. Further, the study observed that the Payables Settlement Period has an insignificant positive impact on Profitability and observed a significant positive impact of the Current Assets Ratio on Profitability. The findings are useful to investors, managers and shareholders when making decisions regarding the firm’s profitability under aforementioned sector. This study is a contribution to the existing body of knowledge on Working Capital Management and it impact on the Profitability of listed companies in the Sri Lankan Consumer Staples Sector since the researchers used the recent data in the data analyzing process. Further, this paper is limited to the analysis of data obtained for five years by forty-six companies only. The time period and sample can further be increased by future researchers in order to broaden up the scope of the study.

INTRODUCTION
Investors all over the world invest their money in a business to get some return on their investment in different forms of business. In small and medium businesses like proprietorship and partnership owners have direct or indirect control over the management of the business. Therefore, they are responsible for all the profits and losses. On the other hand, in the large multinational companies, the managers of the company manage the affairs of the company on behalf of owners and owners of the company need management to take such decisions which will give positive signals to the market, increase the value of the firm, and enhance the profitability. In order to fulfil these expectations, managers should pay attention to maintain their daily operations smoothly. This means they should keep eye on the concept of Working Capital Management. Hence, Working Capital Management is the method a company manages the relationship between assets and liabilities in the short term. The primary objective of Working Capital Management is to enable the company to maintain an adequate cash flow to meet its short-term debts. Therefore, Working Capital Management is an essential concept for every business organization to run its business efficiently. Every business organization in the world highly considered about the concept of Working Capital Management. But currently, e most of the businesses are faced with Working Capital Management issue due to the COVID-19 outbreak. According to Singhania and Mehta (2017), Working Capital is a measurement of operating liquidity, and it describes the short-term position of a company. Further, the inefficient handling of working capital can decline the strength of the entity. Financing decisions that are taken in the short-term, are the basis for the working capital management efficiency and it is necessary for maintaining a proper balance between liquidity and profitability of a firm. Moreover, WCM is all about managing current assets and current liabilities (Panda & Nanda, 2018). WCM is the day-to-day function of all management decisions that affect the size and effectiveness of the working capital (Kaur, 2010).
And the Profitability is the ability to make a profit from all the business activities of an organization. It shows how efficiently the management can make a profit by utilizing all the resources available in the organization (Sandhar & Janglani, 2013). Maintaining liquidity on daily basis in business operations is crucial. It is a difficult task for managers to make sure that the business is running in a well-organized and advantageous manner. There are inclinations for inequality of current assets and current liability which affects a firm's growth and profitability. Thus, the importance of Working Capital Management cannot be overemphasized in corporate finance due to its direct effect on the liquidity and profitability of the firm.
Therefore, this study is to investigate the impact of Working Capital Management on Profitability with special reference to the Consumer Staples Sector firms in Sri Lanka. Consumer Staples Sector is created to group together all the industries that consumers rely on for everyday necessities. Recently, the Sri Lankan market is boosted by gains in consumer staples by displaying considerable growth potential regarding the Consumer Staples Sector. According to the Global Industry Classification Standard (GICS) Lyngstadaas and Berg (2016) also found the result which is similar to the (Deloof, 2003). Recent research conducted by Kwatiah & Asiamah (2020) have found that inventory management, account receivables, account payables, cash conversion cycle, e current asset, current ratio, and firm size have positive effects on return on assets (ROA) and return on return on equity (ROE) whilst leverage affects them negatively. Further, the most recent study conducted by Alvarez, Sensini, and Vazquez (2021), also found a positive and statistically significant relationship between all components of Working Capital and Profitability. However, Makori and Jagongo (2013)  Further, the findings of this study will be beneficial to several stakeholders such as creditors, shareholders, and management of the selected firms when making decisions regarding the firms' profitability. Through this study, creditors can know whether these organizations are maintained an adequate fund to settle their payables or not. The management of the selected firms will have a better understanding of the firms' current working capital management and their profitability. To the shareholders, this study will be provided a better idea about the importance of working capital management as a critical component of profit generation.
From the academic perspective, in the Sri Lankan context, there's a lack of knowledge regarding this subject matter, especially in the Consumer Staples Sector. Thus, this study will be seen as a contribution to the existing body of knowledge on working capital management and its impact on the profitability of listed companies in the Sri Lankan Consumer Staples Sector. So, this effort will fill the knowledge gap in this area of study.
The paper proceeds from the above introduction with sections organized as follows: next section presents the review of related literature, followed by research methods, findings and discussion. Finally, it presents the conclusion.  Lazaridis and Tryfonidis (2006) Deloof (2003), Garcia-Teruel and Martinez-Solano (2007). Moreover, Tran, Abbott, and Yap (2017 ) have reported a similar result based on a sample of 200 Vietnamese SMEs. On the contrary, Gill, Biger, and Mathur (2010) Lazaridis and Tryfonidis (2006); Garcı´a-Teruel and Martı´nez-Solano (2007). Which means if a firm required more time to convert their inventory into cash their Profitability will be lower. However, research conducted by Gill, Biger, & Mathur (2010) and Alvarez, Sensini, & Vazquez (2021)have found a positive relationship between Inventory Conversion Period and Profitability.

Impact of receivables collection period on profitability
Samiloklu and Demirgu.ns (2008)

Relationship between Receivable Collection
Period and the Profitability is the important for the firms. The shorter the Receivable Collection Period, helps firms to be proactive in settling all payments and to broaden the investment opportunities in other projects to make a profit. Previous researches conducted by Deloof (2003)

Impact of payable settlement period on profitability
Research conducted by Garcia-Teruel and Martinez-Solano (2007) on the Effects of Working Capital Management on SMEs' Profitability is based on the panel of 8,872 SMEs for the period from 1996 to2002. The effect of Working Capital Management on SMEs' Profitability was tested by using the panel data methodology. The authors were unable to confirm that the Number of Days Accounts Payable affect SME's Return on Assets. Because they lost significance when they control for possible endogeneity problems. Gill, Biger, and Mathur (2010) Kwatiah and Asiamah (2020) with regards to the listed manufacturing firms in Ghana also reported a similar result.
The lower the Payable Settlement Period, the better the solvency of the enterprise is, the less it takes the working capital of other businesses and increases the reputation of the firm. Therefore, it shows the profitability of businesses in the future. However, the higher the Payable Settlement Period helps to increase the profitability in short term. As per the previous researches, researchers have found that the Payable Settlement Period has the positive relationship between Profitability Kwatiah & Asiamah (2020). And several studies were concluded that they were unable to confirm the relationship between Payable Settlement Period and Profitability Garcı´a-Teruel & Martı´nez-Solano (2007) and Gill, Biger, & Mathur (2010). Lyngstadaas and Berg (2016) have conducted research on Working Capital Management in Norway based on a sample of 21,075 Norwegian SMEs covering the period of 2010-2013 from using Panel Data treatment with fixed effect regression. They have found a negative relationship between Cash Conversion Cycle and Return on Assets. However, Abuzayed (2012) has conducted research on Working Capital Management and firms' performance in emerging markets with reference to Jordan. The study is based on a sample of listed firms in Jordan for the period from 2000 to 2008. This study has found that Profitability is affected positively by the Cash Conversion Cycle by using several estimation techniques such as panel data analysis, fixed and random effects, and Generalized Methods of Moments(GMM). The equal results have obtained from previous research conducted by Gill, Biger, and Mathur (2010) and Sharma and Kumar (2011) with reference to the USA and India respectively. The most recent research conducted by Kwatiah and Asiamah (2020) with regards to the listed manufacturing firms in Ghana also reported a similar result. Furthermore, recent research has conducted by Alvarez, Sensini, and Vazquez (2021) on impact of Working Capital Management on the Profitability of Argentine manufacturing firms and they have found a positive relationship between CCC and Profitability.

Impact of cash conversion cycle on profitability
Therefore, most of the previous researchers have found that the firms have the positive relationship between Cash Conversion Cycle and Profitability.

Impact of current assets ratio on profitability
Most of the studies have conducted by previous researchers did not pay much attention to the Current Assets Ratio in their studies. According to the previous literature, Lyngstadaas and Berg (2016) have found a positive significant relationship between Current Assets Ratio and Profitability in their study regarding Working Capital Management in Norwegian SMEs. Similar results were found in the most recent research conducted by Kwatiah and Asiamah (2020) with regards to the listed manufacturing firms in Ghana. On the contrary, some researchers have found a negative relationship between Current Assets Ratio and Profitability in the Sri Lankan context. For instance, Jahfer (2015) has found that the Current Asset Ratio is having a negative association with Profitability with reference to the research on the Effects of Working Capital Management on Firm Profitability in manufacturing companies listed in CSE in Sri Lanka. In addition to that, Anandasayanan (2011) has found a significant negative relationship in research on Current Assets Ratio and Corporate Profitability with regards to the quoted public companies in Sri Lanka. Moreover, Current Assets Ratio is used as a control variable in these studies.
As per the previous researches, most of the studies have found that the Current Asset Ratio has the positive relationship with the Profitability. But in Sri Lankan context, most researchers have found the negative relationship between Current Asset Ratio and the Profitability. e Empirical studies in sri lanka Anandasayanan (2011) (Aminu & Zainudin, 2015). However, in this study, the Cash Conversion Cycle Theory has been considered.

Cash conversion cycle theory
The Cash Conversion Cycle theory was developed by Richards & Laughlin, (1980). They have explained how firms can ensure a shorter operation cycle to reduce the implications of poor Working Capital Management. Hence, this measures the length of time between a company's purchase of inventory and the receipts of cash from its account's receivables. The Cash Conversion Cycle theory can be used by the management of firms to forecast how long a firm's cash remains tied up in its operations. The Cash Conversion Cycle theory is the core theory that explains Working Capital Management concerning all concepts and components, spanning from raw materials to finished products and outputs indicating inventory levels as well as to receivables, payment, and the cash component (Kwatiah & Asiamah, 2020). The Cash Conversion Cycle analysis provides more clear insights for managing a firm's working capital position in a manner that will assure the proper amount and timing of funds available to meet a firm's liquidity needs.

RESEARCH METHODS
The main objective of this research is to determine the impact of Working Capital Management on the Profitability of listed companies in the Sri Lankan Consumer Staples Sector. The research is mainly a correlational study that focuses on testing hypotheses. To achieve the research objectives, the researchers have followed by a positivism research paradigm and used the deductive reasoning approach. Moreover, this research was performed in a quantitative research approach since it is used quantitative research methods for data analysis purposes.

Data and sample
Sharma and Kumar (2011) India Jahfer (2015) Sri Lanka Products. This study is adopted to the total population as the sample of the study. Accordingly, the current study is performed as a population study. Six companies were removed from the total population (52 firms) due to unavailability of data. Therefore, final sample consists of 46 consumer staple sector companies which are listed in the CSE. The present study is collected data at the firm level and used the secondary data from the audited annual reports of sample companies for a fiveyear period commencing from the financial year 2014/2015 to 2018/2019 which provided the panel of 230 observations.  (Kwatiah & Asiamah, 2020). Figure 1 presents the conceptual Framework of the study. e

Figure 1: Conceptual Framework
Accordingly, based on the conceptual framework following hypotheses were developed to achieve its research objectives. Five hypotheses were named as A, B, C, D and, E to clear identification.

The empirical models
To achieve the purpose of the study, present study has employed panel data analysis. In order to justify the most appropriate panel data analysis model from pooled OLS, Fixed Effect, and Random Effect Models, the F Test, LM Test, and Hausman Test were used. Therefore, the study found the fixed-effect model as the best-suited model for ROA and GOP. Accordingly, regression equations are illustrated for both ROA and GOP as below.
(1)ROA it =β 0 +β 1 ICP it +β 2 ARP it +β 3 APP it +β 4 CAT it +β 5 FSIZE it +β 6 SGROWTH it +ε it i (2)GOP it =β 0 +β 1 ICP it +β 2 ARP it +β 3 APP it +β 4 CAT it +β 5 FSIZE it +β 6 SGROWTH it +ε it ii Accordingly, ICP used as the proxy for the Inventory. The efficient management of inventory ensures a stable working capital. Therefore, the researchers used ICP in order to measure its impact on Profitability. ARP is used as a proxy for the Accounts Receivables. Proper maintenance of account receivables provides additional importance and efficient collection of accounts receivables to determines both profitability and liquidity of the firm. APP used as a proxy for Accounts Payable which is a partial component of the Working Capital Management. Therefore, Accounts Payable is ultimately supported to measure the efficiency of Working Capital Management. CAT is used as the independent variable, and it is an important measure of liquidity. Using above mentioned proxies provide support to test the research objectives in an accurate manner. Further, the researchers used widely applied two measurements of Profitability: ROA and GOP. These measurements are used by the previous influential studies conducted by (Deloof, 2003) , (Lyngstadaas & Berg, 2016) , (Altaf & Shah, 2018) and, (Kwatiah & Asiamah, 2020).
Also, to reduce the potential biases on results, the researchers control the firm characteristics including Firm Size and Sales Growth. The selection of the control variables is based on the previous research conducted by (Charles, Ahmed, & Joshua, 2018). According to Charles, Ahmed, and Joshua (2018), explained Firm Size and Sales Growth are significant determinants of Profitability. Therefore, to reduce the potential biases on results, the researchers control the firm characteristics including firm size and sales growth. Most researchers used the natural logarithm of total assets or the natural logarithm of sales to measure the firm size, for instance; (Sharma & Kumar, 2011;Tran, Abbott, & Yap, 2017 ;Kwatiah & Asiamah, 2020). But the current study, Profitability (Dependent Variable) is measured through ROA and the second control variable (Sales Growth) is measured by sales. Therefore, to eliminate the correlation issue firm size is measured by the natural logarithm of market capitalization instead of using the natural logarithm of total assets or the natural logarithm of sales.

FINDINGS AND DISCUSSION
This study analyzed the data using panel data methodology iii . With the selection of the appropriate model, this study used the descriptive statistics to identify the behavior of the entire variables of the study. Further, study used an inferential statistic, correlation, and multiple regression analysis to check the direction, strength, and significance of all variables in the study.

Descriptive statistics
According to With the selection of the fixed-effect model as the best-suited model for ROA and GOP, this study tested four main assumptions of panel data analysis: testing multicollinearity, heteroscedasticity, autocorrelation, and crosssectional dependence to confirm that the data fits the basic assumptions of the regression model.
In this study, the researchers tested the correlation between the ICP, ARP, APP, CCC, and CAT. And also, tested with the Firm Size and Sales Growth (Control Variables). However, the researchers obtained the multicollinearity issue between CCC and ICP, CCC and ARP.As a remedy for that, researchers removed CCC from the model. e  After removing the high correlated variable from the model, the researcher runs the model without the highly correlated variable. Thus, the researchers obtained the tested result without the multicollinearity issue. Accordingly, all correlations valued in the correlation matrix table 3 are much closer to zero. This means there is no issue of multicollinearity, thus enhanced the reliability for regression analysis. (Table 3 presents the matrix of correlation of the study.) In order to test the heteroscedasticity for ROA and GOP, this study used the Modified Wald test for Groupwise heteroskedasticity. According to the results, the test rejects the null hypothesis and concluded heteroscedasticity as P-value is less than 0.05 (P=0.0000).
The Researchers run the "Wooldridge test" to check the Autocorrelation for ROA. According to this output, the null hypothesis where there is no serial correlation in the model has been accepted, since the Prob > F = 0.0666 which is higher than 0.05. Therefore, the result concludes that this model has no serial correlation (Autocorrelation). The Researchers also run the "Wooldridge test" to check the Autocorrelation for GOP. According to this output, the null hypothesis has been rejected, since the Prob > F = 0.0000 which is less than 0.05. Hence, the result concludes that this model has serial correlation (Autocorrelation).
In order to test the cross-sectional dependence for ROA and GOP, this study used the Pesaran test. The results of this test concluded crosssectional dependence as p values for ROA and GOP are less than 0.05 which is 0.0001for both models.

Regression results for ROA
According to the regression model (Table 4), e the P value is 0.0000 which is less than 0.05. Thus, the overall model is statistically significant. In this study, the R square value is 0. 3551. This means 35.51 % variance of profitability is explained by ICP, ARP, APP, CAT, FSIZE, and SGROWTH. However, 64.49% of the variance of profitability is explained by other variables that are not included in this study.

Regression results for GOP
According to the regression model (Table 5), P-value is 0.0000 which is less than 0.05. Thus, the overall model is statistically significant. In this study, the R square value is 0. 6383. This means 63.83% variance of profitability is explained by ICP, ARP, APP, CAT, FSIZE, and SGROWTH. However, 36.17% of the variance of profitability is explained by other variables that are not included in this study.
The coefficient value for ICP is -0.0003. That means increasing one day of ICP causes to decrease GOP by 0.0003, while other independent variables remain constant. This result is not significant at any level. Therefore, HA1 is not supported. Accordingly, there is negative insignificant impact of ICP on Profitability (GOP). According to the regression model, the coefficient value for e ARP is -0.0008. That means increasing one day of ARP causes to decrease GOP by 0.0008, while other independent variables remain constant. Result is significant at 1% level. Therefore, this study concluded that there is a significant negative impact of ARP on Profitability (GOP). Above hypotheses testing was made based on the significance level of the relationship between the dependent variable and the independent variables. Hypotheses tested by using the P-value (significant value) of each coefficient of independent variables. The confidence interval of accepting hypotheses is 95%. To achieve this confident interval, Pvalue should be equal to or less than 0.05. If it is not equal to or less than 0.05 alternative hypothesis is not supported. Accordingly, this study found several findings after the testing developed hypotheses. The study found that the Inventory Conversion Period has negative but insignificant impact on Profitability (both ROA and GOP). This means if a firm has lower ICP it caused to increase the Profitability. This is good for the firms, and they can utilize their cash in profit generating activities and can reduce the other cost relating to the inventory maintenance. Therefore, Consumer Staples Sector firms should pay more attention on reducing the ICP to obtain more profitability. This result is aligned with the research conducted by (Garcı´a-Teruel & Martı´nez-Solano, 2007) and (Gill, Biger, & Mathur, 2010). Even though, this result is consistent with the aforementioned researches, but it is differing with the recent study conducted by (Kwatiah & Asiamah, 2020 Moreover, the study observed that the Payables Settlement Period has an insignificant positive impact on Profitability. This is good for the companies in short term. But when it comes to the long term, if a firm can pay their debts easily rather than taking more time, they can enhance the trustworthiness with their suppliers and can build a good reputation among them. This would be more beneficial to get more profitability in future. The same results were obtained by (Gill, Biger, & Mathur, 2010). However, this result is contradictory to some previous studies in literature. Because most of researchers found that APP has a negative impact on Profitability for instance: (Deloof, 2003); (Lyngstadaas & Berg, 2016;Tran, Abbott, & Yap, 2017 ). Other than these findings, the researchers were unable to confirm the impact of Cash Conversion Cycle on Profitability since the variable was removed due to the multicollinearity issue. And finally, the researchers found that there is a significant positive impact of the Current Assets Ratio on Profitability. Current Asset Ratio is rarely used by previous researchers in their studies. And this result was confirmed by the previous studies conducted by (Lyngstadaas & Berg, 2016) ,and (Kwatiah & Asiamah, 2020


Examining the Attitude-Behavior Gap and Adoption Intention of SHS Technology : The Role of Social Influence

Current fuel-based electricity used to fulfill household electricity needs becomes a reason that worsens the global warming. Even though Indonesia is benefited from abundant solar radiation level, the utilization of solar energy as one possible solution is still very poor. This unused eco-friendly energy needs to be investigated by examining consumers’ intention to adopt Solar House System (SHS) technology along with factors affecting it. This study uses Behavioral Reasoning Theory (BRT) consists of values, reasons for adoption, reasons against adoption, attitude, and social influence as variables to predict adoption intention. Further, Partial Least Square Modeling is used to test the hypotheses after collecting 428 data by distributing questionnaire in Bandung Area. The result reveals that social influence is found to play the most significant role in predicting SHS adoption intention, attitude, reasons for adoption, and values. Thus, this study extents our understanding of attitude-behavior gap in the context of green technology as well as the impact of social influence.

INTRODUCTION
At present, the world is facing an extreme environmental change, called as global warming. Worldwide temperature alteration has become a detrimental issue, one of which is brought by the increased emissions of greenhouse gases, particularly carbon emissions (CO2) (Pachauri et al., 2014). These greenhouse gas emissions are set off by the utilization of non-renewable energy sources, such as petroleum that functions to generate electricity. Notwithstanding its contribution to worsening global warming, the counted number of petroleum derivative assets additionally fortifies the motivation behind why alternative energy that can supplant its job must be created. In fact, solar energy is professed to be safe, boundless, and non-polluting (Bachtiar, 2006). This is the thing that lies behind the advancement of different usage of solar-based fuel sources, for example, the solar house system (SHS). In addition to expanding admittance to power and protecting the climate, SHS is also embraced because it is practically liberated from maintenance costs, simpler to work, and more secure than other fuel sources (Akhmad, 2005;Feron, 2016). Therefore, from this account, it is essential to investigate the community's intention to adopt SHS technology.
Numerous written works have explored consumer intention on technology adoption (Chen, 2014;Claudy, Garcia, & O'Driscoll, 2015;Claudy, Peterson, & O'Driscoll, 2013;Wolske, Stern, & Dietz, 2017). These examinations with regards to sustainable power sources generally apply conventional speculations, for example, the theory of reasoned action (Fishbein & Ajzen, 1975) or technology acceptance model (Davis, 1989)-which have been impressively censured for their failures to answer attitude-behavior gap (Westaby, 2005). Thus, current researchers in the same study develop the behavioral reasoning theory (BRT), which gives insights in disclosing the process of consumer's thought to receive or to oppose innovation (Claudy et al., 2015;Claudy et al., 2013;Westaby, 2005). Previous literary works recognize personal factors and contextual influences (known as external conditions like social influences, institutional constraints, or regulatory incentives) that occur under the assumption in which contextual influences cannot be changed and personal factors may be the main factors that influence behavior (Claudy et al., 2013).
However, another study by Westaby estimates that global motives independently influence people's global perceived from social pressure behavior (Westaby, 2005). The reason which deciphers the significance of social influence in inclining people to define the information which later turns into their personal values, beliefs, and habits is the missing component that should be researched in innovating adoption study. Besides, extant studies have discovered proof that social influences have a huge function in forming the perceived usefulness of technology and people's behavioral intention to adopt the technology. Particularly in Indonesia with its collectivist culture, people favor homogeneity and similarity, in which something that is not gone along will be viewed as the inability to bond with the group. The collectivist spirit allows individuals to suggest their own personal values that still be dependent on social norms. Based upon this idea, this study proposes that investigating the function of social influence to serve an improved BRT as a valuable theoretical framework to better comprehend the psychological preparation of innovation adoption and resistance in Indonesia is essential.

Development of the research model
In marketing science, understanding consumer attitude and behavioral intention to innovation has so far become a top research need. The theories usually used to quantify these variables are the theory of planned behavior and the theory of reasoned action. Nonetheless, traditional behavioral intention models have failed to understand the attitude-behavior gap (Fishbein & Ajzen, 1975;Peattie, 2010;Westaby, Probst, & Lee, 2010). In the context of renewable energy, for example, consumers are showing an accepting perspective but the adoption behavior experiences frail dispersion in numerous nations (Claudy, Michelsen, & O'Driscoll, 2011).
A recent model which is an augmentation of TPB, the behavioral reasoning theory, proposes a potential detail for the attitude-behavior gap by including context-specific reasons (Westaby, 2005). This framework adequately accounts for the effect of reasons and separates between the factors for and against consumers' behavior in adoption decisions (Westaby, 2005). Moreover, renewable energy, particularly the solar house system technology, is a high-inclusion item that requires a discerning assessment of the reasons for and against the adoption decision process (Claudy et al., 2013). Consequently, by applying the behavioral reasoning theory, this study is expected to improve the comprehension of attitude and intention formation in the context of solar house system technology. Values are motivational constructs, which allude to alluring objectives that people endeavor to achieve (Schwartz, 2005). Numerous literary works assume that reasoning does not happen autonomously but is influenced by consumer's profound established values (Claudy et al., 2013;Westaby, 2005). Reasoning happens when consumers actuate cognitive processes to develop their beliefs and values. Further, this value information process directly affects the reasons that customers use to legitimize their anticipated behavior (Claudy et al., 2013;Westaby, 2005). Many studies affirm that when consumers see a product is in accordance with their own values, they tend to embrace and accept it (Garcia, Bardhi, & Friedrich, 2007;Kleijnen, Lee, & Wetzels, 2009).
H1a: Consumers' values will positively influence the reasons for adoption H1b: Consumers' values will negatively influence the reasons against adoption Furthermore, values can immediately affect consumers' attitudes since reasons may not be completely activated in certain conditions (Tversky & Kahneman, 1974). This happens when consumers want to be more heuristic or to be simpler in responding to the information process without completely assessing the advantages and dangers in decision making (Tversky & Kahneman, 1974;Westaby, 2005), which means consumers structure an attitude without objectively advocating their anticipated behavior.

Reasoning
The reasoning concept is different from beliefs and values. Beliefs are consumers' emotional likelihood that could bring an expansive range of future results and may not be unavoidably connected to the final decision (Claudy et al., 2013 comprehensions that are connected to behavioral explanation. Reasons allude to a thin center that particular variables are important for consumers' behavioral set and influence the purchase decision (Claudy et al., 2015;Westaby, 2005). For example, consumers may firmly accept that utilizing an eco-accommodating product would assist them in preserving the environment. Nonetheless, they may choose not to adopt the product due to the lack of funds. Thus, the following hypotheses are formed: H3a: Consumers' reasons for adoption will positively influence their attitudes towards adoption H3b: Consumers' reasons against adoption will negatively influence their attitudes towards adoption However, reasons may legitimately impact behavioral intention without relying upon the complete process of global motives (experiencing the way toward framing perspectives). Reasons in BRT characterize past intentions that are clarified by global motives alone (Gupta & Arora, 2017). Also, the traditional models have been impressively censured for their inability to explain customer resistance from innovations (Garcia et al., 2007;Ram & Sheth, 1989). It shows that context-specific legitimations have an essential part in forming intentions. In this manner, the following hypotheses are proposed: H4a: Consumers' reasons for adoption will directly and positively influence adoption intentions H4b: Consumers' reasons against adoption will directly and negatively influence adoption intentions

Attitude
The behavioral reasoning theory sets that the key determinant of consumer's adoption intention is attitude. Attitude is a mental inclination with some level of favor or disfavor which influences behaviors (Westaby, 2005). Numerous studies with regards to environmentally friendly power energy conducted in Australia and the US have affirmed the positive relationship between attitude and adoption intention (Paladino & Baggiere, 2007;Wiser, 2007). It shows that consumers' likelihood to shape an intention to lastly adopt a renewable energy technology is reflected in their attitude towards technology.
H5: Consumers' attitudes will positively influence adoption intentions

Social influence
The behavioral reasoning theory also propounds social influence (subjective norm) factor as global motives along with attitude and perceived control as the primary antecedents of intention (Westaby, 2005). In spite of the fact that this variable has various names (subjective norm in TRA, TPB, TAM2; social factors in MPCU; and image in IDT), each construct contains the idea that someone's behavior is influenced by his perception that many important people to him or a particular social circumstance urge him to perform certain behavior (Venkatesh, Morris, Davis, & Davis, 2003). The relationship between social influence and behavioral intention has been tested by many studies and the results are proven in the context of energy-efficient products (Ha & Janda, 2012). Therefore, the following hypothesis is proposed: H6: Social influence will positively influence the adoption intention Attitude concerns with an individual's belief with respect to the results of undertaking a particular behavior as a component of the individual's valuation of the outcomes. Besides being created by behavioral beliefs (Ajzen, 2002), social pressure may likewise impact people to have a positive or negative attitude towards environmental protection. This thought is in accordance with the result of a study conducted in the UK about green electricity adoption (Ozaki, 2011). Along these lines, the hypothesis proposed is: H7: Social influence will positively influence consumer's attitudes towards adoption Literary works assume that pro-environmental values presumably come first before proenvironmental behavior (Pickett-Baker & Ozaki, 2008). For example, to create environmental solutions, people accept that generous exertion is required to lower the usage of energy and preserve the environment (Niemeyer, 2010). Be that as it may, studies find a 'value-action gap' since people decipher and react to similar environmental information in unpredictable and various manners (Blake, 1999;Gadenne, Sharma, Kerr, & Smith, 2011). For this situation, it is inevitable that others' understanding and assessment may likewise impact a person in characterizing the information which later turns into his own values.
Hereinafter, it is normal that reasoning is affected by values (Claudy et al., 2013). Appropriately, it is additionally sensible that social influence directly affects reasoning without experiencing the values. Consumers could get any information about the environment from individuals around them and actuate their cognitive processes to make reasoning (Westaby, 2005). Consequently, the following hypotheses are proposed: H8a: Social influence will positively influence the reasons for adoption H8b: Social influence will negatively influence the reasons against adoption H9: Social influence will positively influence consumers' values

RESEARCH METHOD
The design of this study is causal to comprehend the relationship between variables (Suhartanto, 2014). The information gathered is the primary data with the sample of n = 428 from the greater city of Bandung. The respondents were examined concerning their intention to adopt solar house system technology. 202 out of 428 respondents are male (47.2%) while the other 226 are female (52.8%). In terms of age, the respondents were relatively diverse, with ages 18-25 being 188 (43.9%), 26-33 being 62 (14.5%), 34-41 being 60 (14%), 42-49 being 65 (15.2%), and 50-57 being 53 (12.4%).
The SHS adoption intention variables were measured by using a five-point Likert scale, ranging from strongly disagree (1) to strongly agree (5). Also, partial least squares structural equation modeling (PLS-SEM) was used to verify the structural model and to test the proposed hypotheses (Hair, Sarstedt, Hopkins, & Kuppelwieser, 2014). The model testing included the evaluation of internal consistency as well as convergent and divergent validity of the instrument. To indicate that the construct determines values of the measured and the representative of indicator variables, composite reliability, average variance extracted (AVE), and correlations among latent constructs were also tested.

RESULTS
The assessment of PLS-SEM can be conducted through two methodologies, which are the assessment of the model measurements and the evaluation of the structural model. The assessment of the model measurements should be possible by analyzing the reliability and validity of the construct. To affirm the reliability, the standardized indicator loadings must be 0.7, yet greater than 0.4 can still be accepted (Hair, Sarstedt, Ringle, & Mena, 2012). Further, the value of composite reliability (CR) must be greater than 0.7 to ascertain internal consistency reliability. Meanwhile, the assessment of validity encompasses the evaluation of convergent validity and discriminant validity. Convergent validity can be measured through the average variance extracted (AVE) value that must be greater than 0.5 (Hair et al., 2016). Based on these criteria, Table 1 shows that this study has fulfilled the requirements related to model measurement evaluation. Based on the calculation of the path coefficient in Table 2, it shows that the value on reasons for adoption (β = 0.461) and the value on attitude (β = 0.223) are significant; thus, H1a and H2 are accepted. Conversely, the value on reasons against adoption (β = -0.040) is not significant, so H1b is rejected. Further, the reasons for adoption (β = 0.361) and the reasons against adoption (β = -0.123) on attitude, as well as the reasons for adoption (β = 0.171) and the reasons against adoption (β = -0.107) on adoption intention are significant; thus, H3a-H4b are supported. H5 is also accepted, seen from the coefficient value of attitude on intention (β = 0.245) which is significant. Moreover, social influence on intention (β = 0.359), social influence on attitude (β = 0.225), social influence on reasons for adoption (β = 0.175), and social influence on value (β = 0.433) indicate that H6, H7, H8a, H9 are accepted. On the contrary, H8b is rejected because social influence on reasons against adoption (β = -0.041) is found not significant.

DISCUSSION
The results of this research uncover that value has a positive and significant influence on the reasons for adoption (H1a). This supports the previous studies that value plays a significant part as an antecedent to frame reasoning and attitude (Karahanna, Agarwal, & Angst, 2006). Moreover, value is confirmed to have a positive and significant influence on attitude towards adoption (H2). This happens on the grounds that consumers may want to over-simplify their information processing, known as heuristic motives. Value, additionally, influences attitude via reasoning, which demonstrates a more profound degree of effect attitude via reasoning (Westaby, 2005). Nonetheless, in this study, value does not impact the reasons against adoption (H1b). This happens on the grounds that the reasons for and against adoption are not opposing, but they are different constructs that influence consumers' adoption in different manners (Claudy et al., 2015). In this finding, consumers activate cognitive processing to develop their own personal values to frame their reasoning for adoption. When they see that SHS is as per their values, it reinforces the explanation behind them to adopt it. The values they believe, in any case, do not influence impediments or obstructions they face to adopt the technology.
Furthermore, this research centers on the reasonings (for and against) that have been infrequently tried in empirical studies about the adoption of innovation. The findings report that the reasons for and against adoption significantly influence attitude (H3a; H3b) and adoption intention (H4a; H4b). As discussed earlier, reasoning turns into the solid legitimization component to help the agreeableness of their anticipated behavior or decision. Reasons may likewise straightforwardly influence adoption intention without relying on the whole process of decision making (Westaby, 2005). This clarifies why, sometimes, customers have a positive attitude, but they might still decide against adoption because of a crucial reason like an incompatibility barrier.

Figure 2. Summarized result
Consequently, the findings of this study determine past research proposing that attitude affects adoption intention (H5). It explains the thought that the higher the customer's attitude towards adoption, the higher their chance of forming an intention to finally adopt it. Research in Swedish households affirms that positive attitudes are the principal indicator of purchasing green electricity (Hansla, Gamble, Juliusson, & Gärling, 2008).
This study additionally underscores the crucial part of social influence in affecting adoption intention (H6). The outcome implies that somebody's intention to adapt SHS technology might be molded by the amount of others' environmental endeavors that she sees and she clings to, that trigger her to also contribute to preserving their environment. Additionally, this finding is in accordance with a study in German which affirms that norm is a huge determinant of someone's ability to take an interest in community energy (Kalkbrenner & Roosen, 2016). Thus, consumers can refer others to encourage them in adopting SHS technology.
Moreover, social influence is demonstrated to be noteworthy on consumers in shaping a positive or negative attitude towards SHS adoption (H7). This finding is in line with the study of consumer environmental behavior in Australia (Gadenne et al., 2011). Other than that, social influence additionally affects consumers' values and their reason for adoption (H8a; H9). The study finds out that others' assessments can supplement the different individual perceptions and values regarding SHS reception (Gadenne et al., 2011). Social pressure can also influence one's reasoning to adopt SHS technology. Conversely, social influence is discovered to be inconsequential to the reasons against adoption (H8b). This case is comparative with values influencing reasoning, which happens since the reasons for and reasons against adoption are built to be opposing with each other. Along these lines, social pressure does not influence their obstructions to not adopt the technology.

MANAGER IMPLICATION
Despite the fact that SHS is demonstrated to be environmentally and economically productive since the asset resolved-solar in Indonesia is plentiful, the use of solar energy is still limited. This gap between positive attitude and reluctance to adopt already has not been surely known, but whenever left examined, will keep on hampering the dispersion of sustainable power sources in the market (Prothero & Fitchett, 2000). This research results that attitude, reasons for adoption, and reasons against adoption affect SHS adoption intention. All things considered, this study finds that social influence has a part in affecting the adoption intention and the forming factors, including reasoning. It is recommended that business designers or solar panel companies to maximize the social influence factor in their business activities.
Solar panel companies and business engineers ought to underscore the social influence in their web-based media, which is at present the most advantageous promotional media. Other than giving information about the advantages and features of the product, sharing the testimonials is also a beneficial strategy. Featuring the customer testimonials in social media posts permits different customers to see the advantages of SHS. Besides, SHS technology is a people's high-inclusion product, which is a great idea to allude to different consumers who have utilized it as a wellspring of product assessment. Through this, it is expected that consumers can build more reasons to adopt the technology.
In addition, other than focusing on the product, sharing the campaign to use solar energy is also an important social mission to educate people regarding the environment. This will embrace the personal values and shape an advanced personal awareness regarding environmental conservation, which in the end, frames consumers' positive attitude toward SHS adoption. This strategy is in line with the research findings that personal values, reasons for adoption, attitude, and adoption intention will be affected by social influence.

LIMITATION AND FUTURE RESEARCH
This study just centered around the society who lives in the greater city of Bandung which suggests that this investigation could not speak for the entire Indonesian society. Future studies may test the comparable model in terms of renewable energy in different regions for more improved discoveries. Moreover, quantitative data is the main information utilized in this research. Thus, qualitative data obtained from interviews and focus group discussion is essential in deciding the stronger builds and more composed results. Last, future research with different samples is needed to expand this study and imperative implications


THE ROLE OF FINANCIAL SUPPORT FOR THE PERFORMANCE AND SURVIVAL OF MICRO-ENTERPRISES

Purpose – to examine the Latvian micro-enterprises having indicated the external financing as an important factor for their development. Research methodology – the results of the ad hoc survey (WAPI) on companies registered in Latvia in nationally defined sectors are used. Valid responses were received from 2.511 companies, of which 1.879 were micro-enterprises, the results were processed by using the SPSS programme. Findings – micro-enterprises that have not received the necessary external financing in previous years were less sustainable in the later period. Of the liquidated micro-enterprises examined, 16% were closed in 2020. Research limitations – the study highlights the impact of the availability of finance factor on the survival of micro-enterprises. Practical implications – the findings are useful for business support policy makers to identify preventative measures to ensure the resilience of micro-enterprises in times of economic turmoil when the spread of the Covid-19 has affected economy. Originality/Value – although scientific research on the need for financial support for companies has already been conducted in recent years, our study emphasizes the importance of access to finance for micro-enterprises.

Introduction
Small and Medium Enterprises (SMEs) are recognized all over the world as backbone of modern economies because they make major contributions to global economic growth and sustainable development through employment generation, poverty alleviation, wealth creation and food security (Peter et al., 2018). According to the World Trade Report (World Trade Organization, 2016) in developed countries, SMEs account for more than 90% of enterprises, contributing 60-70% of employment and 55% of gross domestic product (GDP). In turn, the OECD report showed that SMEs could provide up to 45% of total employment and 33% of GDP in emerging countries (Organisation for Economic Co-operation and Development [OECD], 2017). According to the findings of the Small Business Administration 78.6% of newly established businesses between 2005 and 2017 survived one year (Small Business Administration [SBA], 2018). Unfortunately, only about half of these companies have a business life of five years. In turn, only one in three small businesses typically reaches ten years of operation. Although the data presented here refer to the United States, other studies show a similar trend worldwide (Erskine & Yong, 2020).
The aim of our study is to find out the importance of financial support for the development of micro-enterprises from the point of view of entrepreneurs themselves and the reaction of financial employers, promoting the availability of financial support for micro-enterprises, which is the largest share of SMEs in Latvia. The study focuses on the availability of financial support in Latvia for micro-enterprises in accordance with the European classification system (European Commission, 2003). Micro-enterprises make up 94% of all economically active enterprises in Latvia (Central Statistical Bureau of Latvia, 2020).
According to the OECD (2020), the SME lending sector in Latvia is dominated by banking sector lending, which accounted for 74% (at the end of 2018) of total lending to local non-financial corporations (NFCs). Although loans to the SME banking sector decreased by 8.3% in 2018, excluding one-off effects, the volume of loans to SMEs did not change significantly (-1.0% year-on-year). In 2018, new loans (flow) to SMEs were slightly higher than in 2017 (3.9%). In 2018, the new lending (flow) to SMEs was slightly higher than in 2017 (by 3.9%). Over the period covered by the OECD assessment, the overall economic environment remained favorable, supported by rising investment and domestic demand. Risk and growth capital in 2017 increased from 79.4 million euros to 120 million euros. In 2018, 3 new acceleration funds were introduced to the market in addition to several seed, start-up and growth capital funds to promote the development of venture capital investments. Currently, the distribution of state support programs continues through the JSC Development Financial Institution Altum (ALTUM), which offers assistance and financial instruments to various target groups, including micro enterprises. The government facilitates access to finance (through a microcredit, start-up and loan program) for companies that lack the financial credibility (collateral, net worth, cash flow and credit history) needed to access finance from commercial banks or private investors (ALTUM, n.d.). ALTUM's task is to implement state aid programs to compensate for market failures that cannot be remedied by private financial institutions.
The results of a business survey are used in this article. A computer-assisted web interview (CAWI) questionnaire was sent to Latvian companies with publicly available e-mail addresses in the period from January 10, 2018 to January 25, 2018. The request to complete the questionnaire was addressed to the person in charge of corporate finance. The target audience was all Latvian companies operating in sectors eligible for state aid. The entire studied segment included all active enterprises registered in the Latvian Register of Enterprises with 11 defined NACE codes, i.e. a total of 32 308 enterprises. To improve representativeness, data were evaluated by industry share. The ad hoc online business survey (WAPI) asked entrepreneurs to disclose their sources of funding for the three-year period 2015-2017. Valid responses were received from 2511 companies, of which 1879 were micro-enterprises. Respondents identified the diversity of financial sources and answered whether they needed additional funding for their performance in the near future. Previous study based on this survey had shown alarming results: according to the data processed by the SPSS, micro-enterprises most often chose bank financing (short-term and long-term -11%) among many sources, while only 4% of respondents used loans from the financial institution ALTUM (which is the principal intermediary of state aid in Latvia). In addition, the study showed that although almost half of the micro-enterprises needed new or additional funding, a large part of them relied solely on internal finances (Beizitere et al., 2020b). This article provides an in-depth analysis of the reasons for refusals by financial institutions from the point of view of entrepreneurs. In order to find out the impact of the financial shortage in the previous years on the future operation of micro-enterprises, the sample of micro-enterprises from the survey was additionally analysed. This group (n = 667) showed that access to finance has been an important factor for their growth. Among the liquidated companies, most relied on internal financing, but only a few had received a loan from a bank or finances with public support. Of the liquidated micro-enterprises examined, only 16% closed down in 2020 (which may have been affected by the business restrictions imposed by the coronavirus Covid-19).

Theoretical findings
Academic research is devoting a lot of attention on microenterprise financing including important aspects of several stages of company development (Prijadi et al., 2020) and on financing of microenterprises (Hartungi, 2007). SMEs are a powerful economic engine in many European countries (Moya-Martinez & Pozo-Rubio, 2020), substantial contributors to employment and to the GDP growth in many countries , SMEs and employment creation are very important for countries all over the world (Herr & Nettekoven, 2017). Political decisions are often important for business support (Daugėlienė, 2016). Small business is characterised by flexibility, agility, the ability to respond quickly to the slightest changes in economic environment and market requirements (Verovska & Zujeva, 2019). SMEs are not only an important source of employment; they can also become a source of innovation and increased productivity (Herr & Nettekoven, 2017). A very useful material for different stakeholders is publication by the Organisation for Economic Co-operation and Development, for example, "Financing SMEs and Entrepreneurs 2020: An OECD Scoreboard" which provides a comprehensive framework for policy makers and other stakeholders to monitor access to finance by SMEs and entrepreneurs (OECD, 2020).
Finance is the elixir that assists in the formation of new businesses, allows businesses to take advantage of opportunities to grow, employ local workers, and in turn support other businesses and local, state and federal government through the remittance of income taxes (Duff, 2019), the extent to which enterprises have access to finance is an important determinant (Doove et al., 2014). For their development, also the trade credit had a large positive impact on firm survival, such that a one standard deviation increase in trade credit results in a 21% decrease in the likelihood of distress (McGuinnessa et al., 2018). The availability of funding is one of the key problems in the small and medium-sized business not only in Europe but also all over the world economic space (Rupeika-Apoga & Solovjova, 2016).
The importance of non-traditional, alternative/innovative financing is gaining recognition in both developed and emerging economies throughout the world. SMEs' financing in Europe remains primarily bank based, in spite of many policies proposed to develop alternative financing instruments (e.g., adopting directives on venture capital, improving the transparency and visibility of SMEs on capital markets, etc.) (Rupeika-Apoga & Saksonova, 2018), several specific aspects of micro-enterprise financing are also recognised as specific for green economics (Rouf, 2012). Access to finance has been identified as the most important problem that SMEs face. Lack of access to financing is consistently cited by SMEs as one of the main barriers to growth (Harelimana, 2017), however financial support is a determinant of the success of small, medium and micro enterprises (Rungani & Potgieter, 2018). Government support programmes creates important contextual conditions that facilitate the capacity of SMEs to contribute to development through the production of goods and services and the creation of employment (Peter et al., 2018), and are seen as important tools for enhancing the performance of SMEs. SME financing in Europe is not homogeneous but that different financing patterns exist. The cluster analysis identifies six distinct SME financing types: mixed-financed SMEs, state-subsidised SMEs, debt-financed SMEs, flexible-debt-financed SMEs, trade-financed SMEs and internally financed SMEs. These SME financing types differ according to the number of financing instruments used and the combinations thereof. Furthermore, the types of financing available to SMEs can be profiled according to their firm-, product-, industry-and country-specific characteristics (Moritz et al., 2016). Despite enormous effort by government to foster growth and development in the SMEs sector through various support programmes, the rising failure and underperformance of the SMEs sector suggest a contrary effect (Peter et al., 2018). A crucial element in the development of the SME sector is access to finance for the creation, survival and growth of small businesses. Many governments in developed countries design programs to improve the competitiveness of the local firms.
The main goal of government financial support is to promote business in order to accelerate economic growth (Hartšenko & Sauga, 2013). Controlling for family funding, bank financing, equity of business angels and venture capitalists, industry, size, as well as entrepreneur's characteristics, the results reveal that government guarantees and government equity have a direct effect on new firms' competitive advantage and only an indirect impact on performance (Pergelova & Angulo-Ruiz, 2014). A study (Bertoni et al., 2019) concluded that loans guaranteed by the European Investment Fund had a positive effect on companies' assets, sales and employment. Businesses also had a better chance of survival and less chance of going bankrupt. In addition, the positive impact was stronger for new and smaller companies, which generally do not have a good credit history. There was a greater positive impact on those operating in the service sector than in manufacturing, but the impact did not seem to be higher in high-tech and knowledge-intensive sectors than in low-tech sectors.
In general, the strategic use of financial instruments, such as loans and investments, is key to the success of every business. Financial trends also define the state of the economy on a global level, so central banks can plan appropriate monetary policies (Duff, 2019). Main findings show that alternative financial service providers are competing and often outcompeting the traditional ones at high speed. Conducted empirical analysis shows the most available financing sources except banking products are Friends and Family and different state (including European Union grants) support programmes, Venture Capital and Business Angels (Rupeika-Apoga & Saksonova, 2018). More and more importance is paid to security aspects (Davidavičienė et al., 2019;Raudeliūnienė et al., 2014).
In 2014, institutions of public financial support, non-bank credit institutions and Venture Capital funds increased their share in the micro-enterprises financing (and in the financing of all enterprises). The greatest changes in the structure of the micro-enterprises financing occurred due to the aid granted to small businesses by institutions of public financial support (Prohorovs & Beizitere, 2015) and the trend is continuing now. Other research works emphasize that probability to innovate increases when firms use internal financing and grants. The same applies when funds come from family and friends, while not found conclusive evidence for bank loans (Aiello et al., 2020). Important aspects are also marketing aspects (Batraga et al., 2018) which also often influence decisions on the financing for company.
Several reasons have been identified for SMEs to fail ultimately. Among them, frequently mentioned explanations are financial management skills and performance (Erskine & Yong, 2020), also lack of financial literacy of micro, small and medium-sized enterprises owners/managers is often mentioned among the reasons of their financial exclusion (Beizitere, 2018;Saksonova & Papiashvili, 2021). Research from Korea proves that "financial resources from the Korean government indeed help Korean SMEs survive, but do not necessarily help them achieve higher annual assets and sales growth" (Park et al., 2020). However, when government-based diagnostic and support services are combined with public loan financing, they prove to be effective in enhancing the Korean SMEs' annual assets and sales growth (Park et al., 2020).

Empirical research results and discussion
A survey of the companies was conducted at the beginning of 2018 to find out the possibilities of micro-enterprises in Latvia to obtain financing and, among other things, to identify the most frequently used reasons for refusal. A study conducted so far, based on the above survey, has shown companies have indicated access to finance among the most important 13 factors limiting business activity (Beizitere et al., 2020a). At the same time, external financing was not widely used among micro-enterprises, as according to the survey data processed, micro-enterprises still prefer internal financing (64%) among many sources, whereas only 11% of the respondents used public funding (Beizitere et al., 2020b).
An in-depth study was carried out to find out the discrepancy between financing opportunities in Latvia, including the relatively large financial offer of European Union funds, and the reluctance of micro-enterprises to obtain it. The financing needs of entrepreneurs on the one hand, and the reasons for rejection of financing provided by financiers on the other hand are demonstrated below. The survey consisted of questions, many of which required them to be answered on a scale of 1 to 5 (where 1-restricted but 5-unrestricted).
The survey data processing, reability tests have been done by the data analysis programme in the SPSS environment and report a high Cronbach's alpha coefficient (see Table 1).
The distribution of company's responses according to their needs for additional (external) financing to perform company's activities or to realize the idea is included in the Table 2.
Research results indicate that 43.4% of micro-enterprises in Latvia do not need additional (external) financingthey are ready to reach their company development by themselves, 38.1% of the micro-enterprises in Latvia need additional (external) financing.
There are several ways in possible getting of external financing including the state-owned financial institution ALTUM that offers public support financial instruments such as loans on terms that are easier to enforce than bank terms, various guarantees, including to guarantee the repayment of bank loans, and venture capital funding for fast-growing and innovative micro-enterprises (ALTUM, n.d.). Demand for financing differs by regions of Latvia.
Research results indicate that there are different needs for additional financing by company location. Distribution of company responses on needs for additional (external) financing to perform company activities by regions of Latvia is included in the Figure 1.
Research results indicate that in most of the cases micro-enterprises in Latvia do not need additional (external) financing in more developed regions -Riga, but smaller number of companies -in less developed region Latgale. Many of them are ready to reach their company development by themselves (see Figure 1).
Looking in more detail at the views of micro-enterprises, given the number of employees, additional external funding is needed more for those with 5-9 employees to achieve the company's development (see Table 3).
Many companies has applied to different institutions for external financing including to the state-owned development finance institution ALTUM but many of them were refused funding. The distribution of the refusal aspects of micro-enterprise financing is reflected in the Table 4.
Research data in Table 4 indicate that most of financing refuse reason was insufficient cash flow, followed insufficient collateral and insufficient own capital. Smaller numbers of refuse for financing were related to problems in the company's industry and negative owner reputation or credit history. Note: a -listwise deletion based on all variables in the procedure. Other reasons for a bank or leasing company to refuse to provide financing mentioned by number of entrepreneurs are given in the Table 5. Among the answers provided, there are those that describe the entrepreneur's emotional attitude towards refusal, for example, those that characterize the behavior of an ALTUM employee. However, most of these answers could be reduced to some of the answers listed in Table 4. For example, answer Previous year's balance sheet with a "-" sign, Previous year's deficit, The micro-enterprise declaration was not sufficient proof of income and The company has been operating at a loss for the past 2 years correspond to the general respond Insufficient cost-benefit ratio. The attitude of banks or other financial institutions in refraining from lending to a micro-enterprise would probably be understandable here. In turn, answers Lack of pledge and Inadequate loan percent rate offered refer to respond Insufficient collateral. Obviously, the company had to turn to the financial institution ALTUM and not to the bank to deal with the problem of insufficient collateral.
In order to find out the impact of the financial shortage in the previous years on the future operation of micro-enterprises, the sample of micro-enterprises from the survey was additionally analysed.  A small sample was selected, consisting of micro-enterprises, which answered the question: "What factors significantly limit the growth of your representative's business?" The micro-enterprises that indicated that access to finance has the most significant impact on them were examined. Growth impediments were rated on a scale of 1 to 5. Micro-enterprises that responded to the question as "almost restrictive" (4) and "restrict" (5) are considered to be limited. The total number of micro-enterprises whose access to finance factor limits their growth was 667 or 35% of all surveyed micro-enterprises (n = 1879).
This group (n = 667) showed that access to finance had been an important factor for their growth. In examining the viability of post-business survey, it was found that according to the data of the Latvian Register of Enterprises, some companies (9% of the selection) had problems with continuing their business (see Table 6).
Among the liquidated companies, most relied on internal financing, but only four of micro-enterprises had received a short-term financing or a long-term loan from a bank and five of them had obtained finances with public support. Of the liquidated micro-enterprises examined, only 16% closed down in 2020 (which may have been affected by the business restrictions imposed by the coronavirus Covid-19). It should be emphasized that the majority (77%) of micro-enterprises that were forced to close down had 1-4 employees. The product (electronics) is in the idea stage 1 The representative of the ALTUM replied: "You have enough money for yourself! Capitalia (a financial institution entrusted with granting loans from ALTUM resources) referred to the recommendation not to give money according to ALTUM data!" 1 Previous year's balance sheet with a "-" sign 1 Previous year's deficit 1 The micro-enterprise declaration was not sufficient proof of income 1 Insufficient number of customers 1 I offered an application that performs lunar cycle calculations using astrological methods 1 Inadequate loan percent rate offered 1 Incorrect rejection, such as typos, dots, length marks, etc. 1 The company has been operating at a loss for the past 2 years 1 Negative attitude of ALTUM employees towards the owner 1 The company's field of activity is construction services 1 The Latvian state is not interested in the development of small business 1 Frequent reason for refusal that the company is older than 5 years 1 Tax debt 3 1 Lack of pledge 1

Illiquid equipment 1
In the opinion of bank "financial analysts" will not be able to return, because the cash flow was not ideal in the last year 1 Does not support the tourism industry 1 Total number of responses from entrepreneurs of micro-enterprises 17 5 Suspension of economic activity 6 Insolvency proceedings 4 Legal protection process 1

Conclusions
Academic research has shown that there are several ways to get support for company financing, and they analyze widely the ways to overcome problems with company financing by finding various innovative solutions. In previous years, less than half (38%) of Latvia's micro-enterprises needed additional external financing for development. Among them, there are fewer (36%) relatively small micro-enterprises with one to four employees that need additional funding.
Overall, a small proportion (9%) of micro-enterprises for which access to finance was essential for their operations had problems in continuing their business in the period following the survey of enterprises. However, among these companies, a large part of the smallest micro-enterprises (considering the number of employees 1-4) were forced to close down their business in 2018-2020.
Refusal of financing was mainly due to insufficient cash flow, insufficient collateral and insufficient own capital. The lower number of refusals was related to problems in the company's industry and negative owner reputation or credit history.
The results show that financial donors have been very cautious in financing micro-enterprises. It is possible that many micro-enterprises could avoid certain types of refusals by turning to the financial institution ALTUM. ALTUM offers programs with public financial support, for example, in cases with insufficient collateral, or in the start-up phase when financial indicators are not sufficiently stable.
Despite Latvia's policy to improve access to public finances, including support for micro-enterprises, there have been few targeted measures and their opportunities have not always met their intended targets. In the past, there has been no popular public supported financing instruments among micro-enterprises, although the terms of financing programs offered by the government have been less strict than those for bank lending.