Does the Way Variables Are Calculated Change the Conclusions to Be Drawn? A Study Applied to the Ratio ROI (Return on Investment)

Abstract

This research aims to analyse the financial performance of companies using one of the most used profitability indicators, the return on investment (ROI), which measures the company’s performance in terms of the profit generated over time. To this end, several different methods are used to calculate the ROI indicator, considering the different calculation methods used by different authors over the years. The use of different ROI calculation formulas has been identified in the literature, leading to different conclusions. Based on a sample of 2805 Portuguese companies, it examines how the different indicators react to the different variables analysed, using nine different econometric models. Through this study, it is possible to verify that the different variables that depend on the return on investment have different results, namely that the variables “age” and “size” have a negative effect on the return on investment. On the other hand, “financial leverage” and “ROA” have a positive impact on the contribution to the return on investment. We also found that the different variables behave similarly for virtually all types of ROI calculation, although not completely harmonious, especially in terms of impact. The results are empirically vital, as they alert researchers and companies to the need for standardised formulas for calculating variables such as ROI so that results are not distorted. Using one to the detriment of the other impacts the results obtained and the analyses to be carried out. How empirical research will continue to use the ROI metric will always depend on its users’ discretion and free will.

1. Introduction

The concept of performance is used in different fields of activity and measured in various ways to analyse and evaluate something’s performance. Other dimensions of performance exist, such as innovative, productive, marketing, financial, environmental, economic, and social performance, as mentioned in the works of Liu et al. (2018); Giovannoni and Maraghini (2013).

According to Mohammed (2020), a company’s financial performance measures its financial position in a given period and its ability to manage and control its resources. In other words, economic performance is a company’s ability to generate profits. To better analyse it, researchers, who generally use data from financial statements, use various indices such as profitability, solvency, liquidity, efficiency, and leverage.

The profitability ratio is an index used to measure and examine the financial performance of a company and reflects the company’s ability to generate profits. According to Rahmadi et al. (2023); Nurfitriana and Rahadi (2021), profit is considered the most common measure of a company’s performance. Several variables are used to calculate this financial performance indicator, such as ROA (return on assets), ROE (return on equity), EBIT (earnings before interest and taxes), and ROI (return on investment), as mentioned by Adi and Daryanto (2021); Tanko et al. (2021); Rahiminezhad Galankashi and Rafiei (2021).

According to the existing literature, return on investment (ROI) is one of the most used metrics to analyse the efficiency of a company’s financial performance. According to Rahiminezhad Galankashi and Rafiei (2021); Mohammed (2020), this metric is relatively easy to understand and calculate and is based on data from financial statements. It represents objective and tangible results and is one of the most used financial performance indicators. The main objective of this study is to analyse the economic performance of a sample of Portuguese companies using the ROI ratio. Different conclusions are reached using different methods presented in the literature to calculate ROI. In this way, and this is our main contribution to the existing literature, we will use the different ROIs as different dependent variables and, therefore, different econometric estimations. Using these different calculation forms, it will be possible to analyse the differences between the model’s estimations and understand whether the conclusions between the estimations differ depending on the ROI measure used.

In the literature, we can find different studies that use different ratio specifications, but no ratio as ROI accounts for so many other ways of measurement. This study’s relevance is related to the fact that it incorporates different ways of calculating the ROI variable and thus examines the differences that may arise in the conclusions drawn. Also, we intend to shed light on understanding which variables are most important to be used when related to policymaking at the company level. Moreover, with this article, we attempt to fill a gap in the existing literature because, as far as we know, there is no academic literature that tries to find such detailed evidence on the relationship between different ways of calculating ROI and variables as necessary to companies as their size, age, and sales growth. The main conclusions are that the size of a company and its age negatively affect the profitability of its investments. In contrast, using debt to finance investments facilitates realising returns on these investments. The use of debt to finance investments is still better than the use of equity.

Following this introduction, the article is organised as follows. Section 2 gives a brief overview of the current literature on this topic. Section 3 presents the data, variables, main statistics, and correlations, while the following section contains the empirical analysis, model specification, and estimation methods. In Section 5, we discuss the results, and in Section 6, we outline some policy implications.

2. Literature Review

Profit is one of the most common metrics used to analyse a company’s performance (Nurfitriana and Rahadi 2021). According to Mohammed (2020), financial performance can be evaluated using some information from financial statements. He explains that several indices measure a company’s financial performance and can be divided into five categories: profitability index, solvency, liquidity, efficiency, and leverage. More specifically, profitability indices, which are the focus and will be analysed in this study, measure a company’s performance based on the profit generated over time, with indicators such as ROA, ROE, EBIT, and ROI.

Several articles have analysed the financial performance of companies (Detthamrong et al. 2017; Tanko et al. 2021; among others), this performance for several countries and have come to some identical conclusions, even for different countries, e.g., that the size of the company has a negative relationship with the financial performance of companies.

In a more specific analysis, given the objective of this research, several different calculation methods were found for one of the other factors of a company’s financial performance, in this case, return on assets. We can read about these differences in the calculation of this ratio, for example, in the works of Zamfir et al. (2016); Nasrallah and El Khoury (2022); Abid (2023); Dadd and Hinton (2022); Mohammed (2020); Nurfitriana and Rahadi (2021); Adi and Daryanto (2021); Xu and Liu (2021). In the existing literature, ROI is calculated in different ways. The article by Mohammed (2020), for example, calculates ROI by dividing the difference between the return on an investment and the cost of that investment by the cost of the investment. On the other hand, Nurfitriana and Rahadi (2021) argue that the return on investment is used to check the efficiency of that investment and calculate the return by adding the EBITD and depreciation and dividing it by the value of that investment. Rehman (2017) computed ROI by taking the quotient of the average between the EAT (earnings after tax) of year t and the EAT of the previous year (t − 1) and the average between the net equity of year t and that of the last year (t − 1) and concluded that the aggressiveness of financial managers in terms of monetary policy is hostile, while aggressiveness in terms of investment policy has a positive effect on the company’s performance. He also concluded that the economic performance of companies in Pakistan has declined over time, as a correlation between the age of the companies and this performance could be proven.

In their various studies, the authors focused on different areas depending on their research focus. For example, Cezar et al. (2020) analysed the impact of uncertainty on international investment using a panel data regression between 2000 and 2015 and concluded that an increase in uncertainty delays frontier flows. Adi and Daryanto (2021) examined the impact of the COVID-19 pandemic on the financial performance of food and beverage companies listed on the Indonesian stock exchange between 2015 and 2019. The results show a decline in the companies’ profitability index (measured by return on investment, ROI, and return on equity or operating return on equity, ROE), activity index, solvency, and overall financial health after the COVID-19 coronavirus pandemic. However, the difference between before and after the pandemic was not significant. In this study, the authors used the ratio between EBITDA and capital to calculate ROI.

Omran et al. (2021) examine the relationship between performance measurement and the ability of external market participants to evaluate the effectiveness of strategic management quality for Australia and find that the origin of a company’s non-financial performance measures indirectly and significantly influences its financial performance through the implementation of quality-based strategies. Additionally, industrial organisations that emphasise a quality strategy disclose more information on non-financial performance measures in their annual reports, and only organisations that adopt a quality strategy do performance measures positively impact operational and financial performance. In this study, ROI is defined as the profit divided by the investment cost, and Shin et al. (2018); Cheng (2011); Tran et al. (2019) calculate it similarly.

From the work of Ferragina and Iandolo (2022); Osei-Adu et al. (2022); Mashavira et al. (2022); Nasrallah and El Khoury (2022), and many others, the ROI variable can be used in a variety of fields and to analyse a variety of topics. Gender, experience, education, and exposure to Covid 19 are statistically significant variables in models where ROI is the explained variable.

Regarding the variables that we intend to measure their impact on each ROI, the “size” variable is measured by the natural logarithm of each company’s assets (Mohammed 2020), the “age” variable refers to the number of years the company has been in operation (Touny and Shusha 2014). The variable “CG” is the variation in one year’s sales from the previous year’s sales (Rehman 2017).

Based on previous studies, explanatory variables such as company size, growth, and capital structure are expected to have positive relationships with financial performance, which, in this case, the return on investment indicator confirms. Moreover, as we have already mentioned, the literature consensus is that variables such as firm age have negative relationships with return on investment (Fan et al. 2017; Kumari 2021; Rehman 2017).

3. Data, Variables, Main Statistics, and Correlations

The sample used in this study covers the period 2012–2020 for 107,442 Portuguese companies in the property sector (CAE 68-Atividades Imobiliárias). The industry was chosen considering the difficulties faced by these companies during the analysis period and are Portuguese firms once we did not find any other study applied in this setting. As previously mentioned, the objective is to understand whether the different methods used to calculate the ROI indicator impact the results obtained from this broad group of companies. The data used for the study come from the SABI database (financial information of Spanish and Portuguese companies).

Table 1. Variables description.

Abbreviations	Variable Description	Nature
S	Sales	Numeric
A	Assets	Numeric
L	Liabilities	Numeric
EC	Equity Capital	Numeric
OR	Operating Result	Numeric
IBT	Income Before Tax	Numeric
NR	Net Result	Numeric
CL	Current Liability	Numeric
EBIT	EBIT	Numeric
Dep	Depreciation	Numeric
EBITDA	EBITDA	Numeric
AP	Accounts Payable	Numeric
CF	Cash Flow	Numeric
FI	Financial Investment	Numeric

Source: authors’ elaboration based on data collected from SABI.

shows the different variables used to calculate the other ROIs. It should be noted that the values of the ROI were obtained following the literature where these formulas were presented, and no specific treatment was made previously to degrade the results. However, it was noted that after the formula application, there were many existent outliers once the number of missing values was considerably high. Therefore, we proceed with the data treatment in the following manner. We set up cut-off points in the ROI calculations of −99 and +99. Additionally, the ROE variable still presented outlier values, even after eliminating ROI values whose calculated ratios did not fill our limits. In the end, the total sample used for estimations contained 2805 companies.

Seven independent variables explain nine different dependent variables (ROI).

Table 2. Variables used in the study and their calculation formula.

Abbreviations	Description Variables	Method of Calculation	Nature	Authors
${ROI1}_{i,t}$	Return on Investment in Company i in Year t	$\frac{{NR}_{i,t}-\left(A_{i,t}-{CL}_{i,t}\right)-{FI}_{i,t}}{{FI}_{i,t}}$	Numerical	Mohammed (2020)
${ROI2}_{i,t}$	Return on Investment in Company i in Year t	$\frac{({EBITD}_{i,t}+{Dep}_{i,t})/2}{{(A}_{i,t}-{CL}_{i,t})/2}$	Numerical	Nurfitriana and Rahadi (2021)
${ROI3}_{i,t}$	Return on Investment in Company i in Year t	$\frac{({NR}_{i,t}+{NR}_{i,t-1})/2}{{(EC}_{i,t}-{EC}_{i,t-1})/2}$	Numerical	Rehman (2017)
${ROI4}_{i,t}$	Return on Investment in Company i in Year t	$\frac{{EBITDA}_{i,t}}{(A_{i,t}-{CL}_{i,t})}$	Numerical	Adi and Daryanto (2021)
${ROI5}_{i,t}$	Return on Investment in Company i in Year t	$\frac{{IBT}_{i,t}}{{AP}_{i,t}}$	Numerical	Rehman (2017)
${ROI6}_{i,t}$	Return on Investment in Company i in Year t	$\frac{{NR}_{i,t}}{(A_{i,t}-{CL}_{i,t})}$	Numerical	Zamfir et al. (2016)
${ROI7}_{i,t}$	Return on Investment in Company i in Year t	$\frac{{NR}_{i,t}}{A_{i,t-1}}$	Numerical	Dadd and Hinton (2022)
${ROI8}_{i,t}$	Return on Investment in Company i in Year t	$\frac{{CF}_{i,t}-{Dep}_{i,t}}{A_{i,t-1}}$	Numerical	Touny and Shusha (2014)
${ROI9}_{i,t}$	Return on Investment in Company i in Year t	$\frac{{OR}_{,t}}{(A_{i,t}-{CL}_{i,t})}$	Numerical	Ferragina and Iandolo (2022)
${CG}_{i,t}$	Company Sales Growth i in Year t	$\frac{{Sales}_{i,t}-{Sales}_{i,t-1}}{{Sales}_{i,t-1}}$	Numerical	Rehman (2017)
${Age}_{i,t}$	Company Age i in Year t	$Ln{(Age)}_{i,t}$	Numerical	Touny and Shusha (2014)
${Size}_{i,t}$	Company size i in Year t	$Ln{(A)}_{i,t}$	Numerical	Mohammed (2020)
${ROA}_{i,t}$	Return on Assets in Company i in Year t	$\frac{{OR}_{i,t}}{{Assets}_{i,t}}$	Numerical	Abid (2023)
${ROE}_{i,t}$	Return on Equity in Company i in Year t	$\frac{{OR}_{i,t}}{{EC}_{i,t}}$	Numerical	Xu and Liu (2021)
${ROCE}_{i,t}$	Return on Capital Employed in Company i in Year t	$\frac{{IBT}_{i,t}}{[\left[\left(A_{i,t}-{CL}_{i,t}\right)+\left(A_{i,t-1}-{CL}_{i,t-1}\right]/2\right]}$	Numerical	Rehman (2017)
${FL}_{i,t}$	Financial Leverage in Company i in Year t	$\frac{L_{i,t}}{A_{i,t}}$	Numerical	Xu and Liu (2021)

Source: authors’ elaboration.

shows the various calculation methods for our study’s dependent and independent variables.

Using

Table 3. Main descriptive statistics.

Variable	Obs	Mean	Std. Dev.	Min	Max
ROI1	5535	−26.8374	30.6114	−98.9973	98.9494
ROI2	5535	0.0974	1.5391	−77.1246	32.9541
ROI3	5535	0.1576	1.7881	−35.8688	50.3612
ROI4	5535	0.0972	1.5388	−77.1246	32.9541
ROI5	5535	0.6930	6.1633	−95.0080	96.9763
ROI6	5535	0.0148	1.6929	−79.5885	33.1578
ROI7	5535	0.0224	0.4877	−11.3257	18.5831
ROI8	5535	−0.0350	0.1038	−5.4753	0.4806
ROI9	5535	0.0457	1.6472	−77.1246	33.1578
CG	5535	1.1656	7.5070	−1.0000	97.7306
Age	5535	2.3983	0.8490	0.0000	4.5951
Size	5532	13.5213	1.5819	7.4761	18.8094
ROA	5532	0.0084	0.3970	−14.0821	1.6979
ROE	5532	0.1926	2.5843	−55.4936	64.6324
ROCE	5535	0.0371	1.8255	−84.5832	30.4029
FL	5532	1.1376	2.3216	−0.8087	123.2960

Source: authors’ elaboration.

, we can verify the number of observations, the mean, the minimum, the maximum, and the standard deviation of the variables to be analysed and used in estimations. The mean values of the different ROI variables are very different, with the highest (negative) one being that of ROI1 and the highest (positive) one being that of ROI5. The amplitude between the minimum and maximum values for the different ROIs is also very high and differs among the calculated dependent variables. The standard deviation is higher for the ROIs with the highest means within the sample, and on average, corporate growth was minimal within the period analysed. ROA and ROCE reveal shallow values, and financial leverage differs significantly among the 2805 companies in the final data analysis. Finally, none of these companies are relatively new in the market since the average age is around eleven years.

To obtain accurate results from the empirical analysis, we also consider the problem of multicollinearity. The Pearson correlation test (

Table 4. Pearson’s correlation coefficients.

	ROI1	ROI2	ROI3	ROI4	ROI5	ROI6	ROI7	ROI8	ROI9	CG	Age	Size	ROA	ROE	ROCE	FL
ROI1	1.0000
ROI2	−0.0054	1.0000
ROI3	−0.0238 *	0.0602 ***	1.0000
ROI4	−0.0060	0.9998 ***	0.0602 ***	1.0000
ROI5	0.0088	0.0501 ***	0.0082	0.0502 ***	1.0000
ROI6	0.0104	0.9666 ***	0.0694 ***	0.9668 ***	0.0395 ***	1.0000
ROI7	−0.0004	0.0475 ***	0.0139	0.0475 ***	0.1372 ***	0.0364 ***	1.0000
ROI8	0.0577 ***	−0.0357 ***	−0.0500 ***	−0.0357 ***	−0.0008	−0.0135	−0.2699 ***	1.0000
ROI9	0.0071	0.9751 ***	0.0704 ***	0.9749 ***	0.0450 ***	0.9972 ***	0.0423 ***	−0.0152	1.0000								VIF
CG	0.0395 ***	0.0107	−0.0002	0.0107	0.0077	0.0098	0.0067	0.0085	0.0114	1.0000							1.00
AGE	0.0668 ***	−0.0250 *	−0.0655 ***	−0.0244 *	−0.0056	−0.0063	−0.0076	0.1345 ***	−0.0119	−0.0111	1.0000						1.17
SIZE	0.1937 ***	0.0178	−0.0379 ***	0.0178	0.0351 ***	0.0300 **	0.0616 ***	0.1706 ***	0.0286 **	0.0315 **	0.3823 ***	1.0000					1.25
ROA	−0.0364 ***	0.1467 ***	−0.0146	0.1467 ***	0.1795 ***	0.1261 ***	0.3653 ***	−0.0001	0.1333 ***	0.0147	0.0623 ***	0.2059 ***	1.0000				1.39
ROE	−0.0105	−0.0274 **	0.0285 **	−0.0274 **	−0.0015	−0.0284 **	−0.0283 **	−0.0023	−0.0258 *	0.0122	−0.0496 ***	−0.0331 **	−0.0898 ***	1.0000			1.02
ROCE	−0.0043	0.0519 ***	0.0108	0.0519 ***	0.0367 ***	0.0497 ***	−0.0479 ***	0.0076	0.0498 ***	0.0134	0.0182	0.0310 **	0.2054 ***	0.0704 ***	1.0000		1.05
FL	0.0759 ***	−0.0647 ***	0.0192	−0.0647 ***	−0.0502 ***	−0.0558 ***	−0.1488 ***	−0.0291 **	−0.0577 ***	−0.0003	−0.0896 ***	−0.2450 ***	−0.4896 ***	0.0134	−0.1204 ***	1.0000	1.36

Source: authors’ elaboration. Note: *, **, *** significant at 10%, 5%, and 1%, respectively.

) applied to our variables has shown that there is no multicollinearity between the variables considered, considering that we have used the value of 0.80 as a cut-off value, as other studies (Gujarati 2004), except for some high correlations between independent variables that are not used in the same regression. Even so, we have computed variance inflation factors, also presented in Table 4, where a mean VIF of 1.18 was obtained. Therefore, we included all the independent variables in the estimations without risking multicollinearity problems.

In this work, we intend to test the hypothesis that, given the different ways of calculating ROI evidenced in the literature, variables such as company size, age, and turnover growth influence this indicator similarly.

4. Empirical Analysis, Model Specification, and Estimation Methods

There should be a total of 996,978 observations, but since data are missing and many companies only started operating after 2012, we have an unbalanced panel. Three alternative estimation methods with panel data can be used to estimate Equations (1) to (9) (Greene 2005; 2018). Since the nature of the annual data collected is panel data, the panel data regression model will be considered throughout the empirical study. The regressions were performed using the software STATA version 18. The nine regressions performed are as follows:

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{1}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{6}{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(1)

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{2}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{6}{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(2)

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{3}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{6}{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(3)

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{4}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{6}{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(4)

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{5}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{6}{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(5)

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{6}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{6}{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(6)

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{7}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(7)

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{8}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{6}{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(8)

$${\mathit{R}\mathit{O}\mathit{I}\mathbf{9}}_{\mathit{i},\mathit{t}}=\mathit{\alpha }+\mathit{\beta }\mathbf{1}{\mathit{C}\mathit{G}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{2}{\mathit{A}\mathit{g}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{3}{\mathit{S}\mathit{i}\mathit{z}\mathit{e}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{4}{\mathit{R}\mathit{O}\mathit{A}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{5}{\mathit{R}\mathit{O}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{6}{\mathit{R}\mathit{O}\mathit{C}\mathit{E}}_{\mathit{i},\mathit{t}}+\mathit{\beta }\mathbf{7}{\mathit{F}\mathit{L}}_{\mathit{i},\mathit{t}}+{\mathit{\mu }}_{\mathit{i},\mathit{t}}$$

(9)

The first method is the simple OLS approach in the grouped model but has the property that it does not assume specific firm and time effects. This estimation method is more suitable for a homogeneous group of observations, which is different from the case here, as shown in Table 3 of the descriptive statistics. As we can see in the cases of the ROI1, ROI2, and financial leverage variables, the difference between the minimum and maximum values is very high. Another estimation approach that captures the specific heterogeneity of individual companies is the so-called fixed effects (FE) model, which captures this heterogeneity as a constant. The last estimation method applied to panel data is the random effects (RE) approach, which again captures the heterogeneity of the companies in the error term. The estimates presented in

Table 5. Results from the estimations.

Variables	ROI1	ROI2	ROI3	ROI4	ROI5	ROI6	ROI7	ROI8	ROI9
CG	0.0348	0.0004	0.0037	0.0004	−0.0008	0.0001	−0.0003	−0.00004	0.0002
Age	7.1776 ***	−0.1935 **	−0.2193	−0.1935 **	−0.2049	−0.2041 **	−0.1202 ***	0.0612 ***	−0.2152 **
Size	−9.3969 ***	0.0837	0.0475	0.0836	0.1819	0.0921	0.0703 ***	−0.023 ***	0.0852
ROA	18.0884 ***	0.3804 ***	−0.0288	0.3804 ***	3.2541 ***	0.3797 ***	0.4883 ***	−0.0058	0.3807 ***
ROE	0.0282	0.0036	−0.0340 ***	0.0036	0.0098	0.0032	0.0010	−0.0001	0.0046
ROCE	−0.1859	0.0699 ***	0.0275	0.0699 ***	−0.0051	0.0887 ***	−0.0038	0.0003	0.0828 ***
FL	4.3597 ***	0.1450 ***	0.0126	0.1450 ***	0.7876 ***	0.1587 ***	0.0772 ***	−0.0020	0.1542 ***
Constant	77.8275 ***	−0.7422	0.0292	−0.7411	−2.1991	−0.9288	−0.7317 ***	0.1323 *	−0.7733
Hausman (p-value)	0.0000	0.0000	0.0043	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
F (p-value)	0.0000	0.0000	0.1093	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

Note: ***, **, and * denote statistical significance at the 1%, 5%, and 10% level of significance, respectively. Source: authors’ estimations.

were performed with fixed effects from the panel data. Given the F-test, the LM-test, and the Hausman test results in all models, fixed effects are the more suitable choice for the estimation.

As Table 5 shows, six of the nine ways of calculating the ROI show statistical significance for four variables at a level that is normally considered acceptable. Variables with statistical significance are also present in the other three models, albeit in smaller numbers.

5. Discussion

Table 5 shows that each variable’s contribution to explaining each way of calculating ROI is very different. It is impossible to assign a pattern of behaviour, most likely because the way ROI is determined is different in each of the estimated nine models. Despite this fact, some clues can be derived.

It may be a surprise that company sales growth does not significantly contribute to any of the models, which suggests that sales growth does not generate a return on investment.

The contribution is generally negative in terms of company age, which may suggest that as companies age, they struggle to realise returns on the investments they have made. In two models, the contribution is negative, and only in one model is the contribution of company size (measured by volume of assets) positive for investment recovery.

In a way that is considered normal, the ROA variable provides positive and significant contributions to ROI in practically all models, as the investments made by the companies are part of their assets. The ROCE variable also positively contributes to ROI, as explained below. The ROE variable does not contribute to ROI.

The contribution of financial leverage to ROI is positive and significant in practically all models.

6. Conclusions and Policy Recommendations

As we have already mentioned, our study does not aim to identify the most appropriate method for calculating ROI but to analyse the contribution of some variables to the formation of ROI, considering a range of nine possible alternatives most used in the literature. To this end, we have used 107,442 Portuguese companies in the property sector between 2012 and 2020. We can draw some conclusions from the estimates made.

One of the main conclusions we can draw is that financial leverage contributes to the return on investment. This could indicate that using credit to finance investments can increase the size of these investments, which might not be as large when using equity. This is efficient in terms of profitability, as this capital is limited.

Growth in business volume alone does not indicate the profitability of investments in any of the models. It could be because many companies expand their business, e.g., due to an increase in prices, not due to investments.

The age and size of the companies contribute more negatively than positively to the various ROI calculations. This econometric evidence may mean that the larger and older the company, the more complex the ROI is. As for the private sector, managers should bear in mind that the choice discretion of ratio calculations could condition investors’ understanding, and the public sector could feel more difficulty following management strategies considering accountability practices. By the attained results, sole discretion will remain, and stakeholders should bear this fact in mind.

Given the hypothesis under study, we can conclude that, given the different ways of calculating the ROI we consider, the contribution of the company’s size, age, and variation in its turnover affect the ROI differently.

Based on our evidence, our policy recommendations are to review the company’s age, size, and financing of investments so that investors achieve a higher return.

As a point of reference for future work, it would be interesting to see whether this finding also applies to other sectors of the economy, other countries, or even industries that require high levels of investment and in which both equity and debt capital are used.

In our opinion, this study presents a limitation that could modify the results if it did not exist. This limitation is because, for the reasons mentioned, we cannot consider a sample of 107,442 companies. Another recognised limitation is the simplicity of the methods implemented. Therefore, the work would benefit if we improved this method using machine learning instead of an OLS estimator. Alternatively, we could consider using the mixed effect model instead of fixed panel OLS.