The Effect of Golden Ratio-Based Capital Structure on Firm’s Financial Performance

Abstract

This study aims to apply the golden ratio to the capital structure of non-financial institutions in France and the United Kingdom to find the effect of the golden ratio’s deviation from the capital structure on financial performance. A golden ratio is an irrational number with an approximate value of 1.618. In this paper, the golden ratio was applied to develop the assumption that the firm should use debt at a percentage of 61.8% and equity at 38.2%, which deviates from the capital structure variables. The final study sample consisted of 150 non-financial institution firms from France and 200 from the U.K. between 2002 and 2021. In addition, the general method of movement (GMM) was chosen to estimate the effect of capital structure variables deviating from the golden ratio on firms’ financial performance. The study results show that when a firm uses equity at a percentage of 38.2% in its capital structure, it can have a positive and significant impact on its financial performance in both France and the U.K. However, the results show that the debt-to-equity ratio deviated from the golden ratio and had a negative and statistically significant effect on both countries’ TOBQ, EPS, ROA, and ROE. Moreover, the firms’ adoption of IFRS can positively and significantly impact financial performance in France and the UK. Generally, managers in France are encouraged to use 38.2% equity and 61.8% debt in their capital structure. However, managers in the U.K. should apply equity of 38.2% and debt of 61.8%, depending on the performance measurement demanded.

1. Introduction

Finance is the backbone of every business, individual, and entity. Finance is divided into three parts: public finance, individual finance, and, most importantly, corporate finance. Every business is backed by corporate finance. Corporate finance decisions include determining what kind of capital structure mix would suit an organization [1]. Every firm, disregard of its size, needs funds to acquire assets, undertake investment activities, purchase raw materials for their business operations, and pay their workers’ wages and salaries. Therefore, the success of every business is dependent on its financial decisions. An organization’s capital structure is the foundation for any sound investment policy.

Corporations finance their activities with internally generated funds or may require external funding [2,3]. The external funding may come from debt and equity. A corporation’s capital structure is the mix of debt and equity used to fund its day-to-day business and acquire and maintain its assets [4]. When corporations decide on a capital structure, they can either decrease their debt and equity levels or raise them. Deciding on whether to use debt or equity financing and how to settle agency conflicts between shareholders and creditors are two questions that need answers if the corporation is deciding on the selection of a capital structure. According to Berk [5], companies can choose from various capital structure strategies, including using a significant amount of debt financing or a negligible amount. According to the pecking order theory, a corporation should prioritize its funds when determining the sources of finance and use for its operations by considering its internally generated funding at first [6,7,8]. If the funds generated internally are insufficient, corporations should consider using debt financing; equity financing should be their last alternative. Firms may prefer internally generated funds over debt and equity financing [9].

The M & M proposition II also says that when a firm uses more debt than equity, it has a reduced weighted average cost of capital (WACC). One of the cues to determining the optimal capital structure is using WACC. However, there is no fixed percentage of WACC to be used to ensure an optimal capital structure. The use of trade-off theory has been a guide for financial managers when deciding the percentage of debt to be used in the capital structure. The trade-off theory states that a company should not use debt financing when a tax shield benefit would exceed the expense of filing for bankruptcy. When a company’s capital structure is made up of too much debt, it faces default risk, which can lead to insolvency [10]. Therefore, when determining the optimal level of capital structure, the firm should weigh the costs and benefits. The risk associated with a high debt ratio will outweigh any tax benefits that may be obtained. Supposedly the firm’s operating income is insufficient to meet interest charges; in that case, the company may be forced into bankruptcy if the stockholders cannot make up the difference during times of economic crises. Financial leverage reduces a company’s tax liability but raises the default risk for banks, credit unions, and private lenders. A corporation will likely default on its debts and other obligations if it fails to meet the required payment dates [11]. Higher leverage levels increase credit default risk and weaken a company’s capacity to make interest and principal payments.

The golden ratio was used by Luca de Pascoli, Fibonacci of Pisa, to solve a problem regarding an expanding rabbit population. Additionally, two bunnies in a room with a wall on all sides were isolated by Fibonacci. If each pair breeds once a month and the offspring begin reproducing the following month and the curious point was about how many rabbits might be produced from that first pair in a year. As a result, the numbers 0,1, 1, 2, 3, 5, 8, 13, 21, 34, and 55 were obtained.... (Fibonacci left off the first term in Liber Abaci Ⓣ). The fact that each number in this sequence is the sum of the two preceding, and they can be used in a wide variety of mathematical and scientific contexts [12].

Organizations may prefer debt financing to equity financing due to the fixed payment of debt service obligations (interest and principal) and the benefit of a tax shield [13]. Many scholars have argued that when an optimal capital structure is used, it maximizes the shareholders’ wealth [14,15,16]. Miller says that the mix of debt and equity does not affect the firm’s value [17]. Welch and Swanson advised that the firm’s capital structure is optimized when it uses 50% debt and 50% equity [18,19]. Scholars believe that using 50% debt and equity in the capital structure would not benefit the firm. The firm could not enjoy the tax shield benefit and would end up paying the government for their earnings as a tax [20,21].

Properly selecting the percentage of debt and equity in the firm’s capital structure leads to better financial performance. In order to determine the percentage of debt and equity to employ in the capital structure that would benefit the business corporation in achieving higher financial performance, this study used the golden ratio as an optimal capital structure to determine the effect of the golden ratio-based capital structure on financial performance.

Numerous investigations have revealed that capital structure affects company performance [22,23,24,25]. A study on the effect of capital structure on financial performance discovered that short-term debt to the total asset has a statistically insignificant effect on ROA, ROE, and EPS but has a statistically significant effect on Tobin’s Q. The study found that long-term debt to total capital has a positive and statistically significant effect on ROA and ROE, while a negative and statistically insignificant effect is found on EPS and Tobin’s Q [26]. Research on the effect of capital structure on financial performance also found that the total debt ratio has a positive and statistically significant effect on the ROA and ROE of non-financial institutions in Germany [27]. The examination of the effect of capital structure on financial performance revealed that the total debt to total asset ratio has a positive and statistically significant effect on ROA and ROE. After moderating the capital structure with governance, the total debt to total asset ratio has a positive and statistically insignificant effect on ROA and ROE [28]. According to another study, the debt ratio has a negative and statistically significant effect on ROA and ROE [29]. All those studies did not apply the golden ratio to the capital structure to find the effect of capital structure on financial performance.

Ulbert [30] used the golden ratio in the capital structure of manufacturing and service companies in the USA and Europe to find out how it boosts their financial performance. The study used total assets, total revenue, net income, and closing price as dependent variables and shareholder equity as independent variables. Extensive studies as to how the application of the golden ratio to the capital structure of firms can ascertain their impact on firm financial performance have not been explored to the best of our knowledge.

The primary aim of this study is to examine applying the golden ratio-based capital structure of non-financial firms in the U.K. and France to find out how the firms’ deviations from the golden ratio impact their financial performance. The golden ratio is used as an optimal and sustainable capital structure. Accordingly, this study seeks to answer the following questions: (1) To what extent does golden ratio-based capital structure affect firm performance in the UK and France? (2) What percentage of debt and equity should a firm use in its capital structure to obtain optimal capitalization? (3) Does IFRS adoption affect firm financial performance?

Consequently, this study has made numerous contributions to the literature. Firstly, investigating the effect of a golden ratio-based capital structure on the financial performance of firms from France and the U.K., where the firm’s debt-to-equity ratio indicates that the firm used a greater percentage of debt than equity. Therefore, based on the principle of the golden ratio, the ratio of two-line segments, one longer than the other, equals the ratio of the bigger segment to the shorter segment. Therefore, the study assumed that 61.8% represented debt, the longest line segment, and 38.2% represented equity, the shortest line segment. Secondly, the study also contributes to the literature by finding the effect of capital structure (EYTRAT, CAPRAT, DEEUTY, STTTTA, and LTTTTA) deviating from the golden ratio on financial performance (ROA, ROE, EPS, and Tobin’s Q), where CAPRAT, DEEUTY, STTTTA, and LTTTTA present debt and EYTRAT presents equity, where their results have not yet been discovered in the literature (Figure 1).

The remaining sections of this research are organized as follows: The relevant literature is presented in Section 2. Data and methods are presented in Section 3. Section 4 deals with empirical findings. The key findings and policy implications are discussed in Section 5.

2. Literature Review and Hypothesis Development

2.1. Pecking Order Theory

According to the pecking order theory, developed by Myers and Majluf [6], money flows based on hierarchy. The corporation would instead use internal funding before considering debt and equity financing. Asymmetric information is the theoretical foundation for the pecking order. When one person has access to more or better information than the other, a communication breakdown can occur due to information asymmetry. When corporations use internally generated funding, which comes directly from the firm according to the pecking order theory, it aids in minimizing information asymmetry. Internal financing is the most cost-effective and time-efficient option compared to the costs associated with obtaining external financing, such as debt or equity financing. The pecking order theory says that a corporation considers internally generated funding before considering external funding, such as debt and equity. No percentage was specified in the capital structure concerning debt and equity financing. The golden ratio was used to build on the pecking order theory of the percentage of debt and equity that a corporation can use in its capital structure. The application of the golden ratio indicates that the larger line should be 0.618 and the smaller line should be 0.382. Most firms used a greater percentage of debt financing compared to equity financing. Therefore, in this paper, it was assumed that the debt component in the capital structure should be 0.618 and the equity component should be 0.382 [31].

2.2. Agency Cost Theory

According to agency theory, managers, shareholders, and debt holders have competing interests [32]. For a corporation to maximize its value, it needs to have the best capital structure, and having the best capital structure reduces agency costs [33]. An agency cost exists between the shareholders, management, and debt and equity holders [34]. Company executives consider their interests initially before considering increasing shareholders’ wealth and the stock price for investors because of agency problems. Debt financing is more preferred by managers over equity financing because it costs less to obtain debt and faceless agency problems between the management and shareholders [3].

2.3. Market Timing Theory

Market timing theory says that when deciding whether to issue debt or equity, it is important for a corporation to think about how the market value changes over time [35]. It also asserts that the state of the stock market affects management’s decisions about capital structure or that managers use information from the stock market when deciding how to finance a business [36]. Managers take advantage of a rising market by issuing new shares of stock or selling overvalued shares, whereas falling markets often prompt them to turn to debt financing instead. According to this theory, opportunities in the capital market happen when people do not have the same amount of influence and information about the choice of a financing strategy [37]. When the market price share drops and corporations consider using debt financing, the golden ratio can guide them to the percentage of debt and equity financing they can use in their capital structure.

2.4. Golden Ratio and Its Application

One of the most well-known mathematical concepts, the golden ratio, has deep roots in the Fibonacci sequence. The Greek letter phi (ϕ) stands for the “golden ratio”, or “golden mean”, which is an irrational number with an approximate value of 1.618. When the ratio of two numbers is the same as the ratio of their sum to the ratio of the larger two numbers, a golden ratio will be available. The golden ratio occurs when the ratio of two-line segments, one longer than the other, equals the ratio of the bigger segment to the shorter section. People versed in the Fibonacci sequence will see similarities between the golden ratio and that series. This is because as the number of Fibonacci sequences increases, the ratio between any two consecutive numbers gets closer to the golden ratio [38,39].

The Fibonacci Summation series, named after Leonardo’s nickname, has made him a legend throughout history and will continue to do so into the future. Starting with the numbers 0 and 1, each following number in this sequence will be the sum of the two preceding ones. If you divide any number in the series by the one before it, you will obtain a fraction that asymptotically approaches 1.618. Point C on line AB, where AC/CB = AB/AC = 1.618, is one definition. A similar statement would be that line AB is bisected at point C, with AC equaling 61.8% of AB and CB equaling 38.2% of AB [33]. The deviation from the golden ratio to analyze the debt-to-capital investment ratio was used by Amershi [12]. It is concluded that a company would do well in the future if its debt ratio to total capital was positive. In contrast, a negative value indicated that the company would fail. Discriminatory power was used by them to predict which businesses would thrive and which will fail or resort to fraudulent practices that increase their chances of going down. Given these results, it makes sense to look into how Fibonacci ratios can be used to predict finances and find fraud.

The golden ratio was utilized by Disney [40] to find the optimum gain in the inventory and work-in-process (WIP) feedback loops, allowing for comprehensive visualization of all viable solutions. The golden ratio, used to describe the best behavior in nature, is also used to describe the ideal feedback gain in a production and inventory control system, which is an interesting coincidence. The golden ratio was used as the foundation for buy one get one free (BOGOF) sale by some business researchers, and it was found that the golden ratio could be used as a marketing standard that balances the company’s and its customers’ needs. This claim is buttressed by research demonstrating that when variable costs are mainly in the upper half of the range needed for any of these multi-buy offers to make a profit, golden ratio sizing is more likely to produce better profits than BOGOF or 3-for-2 [41].

In medicine, the golden ratio was utilized to analyze the blood pressure (BP) of people with significant illnesses [42]. Age, sex, smoking status, history of diabetes, congestive heart failure, stroke, and coronary artery disease are all part of the health condition. When their blood pressure was measured and found to be out of the golden ratio, larger numbers suggest that BP ratios vary, while smaller values indicate that they are closer to the golden number of 1.618. Differences in BP readings from the “golden ratio” were found to be independently linked to death from all causes. The effects of a capital structure based on the golden ratio on financial performance and market acceptance were analyzed, and it was concluded that capital structures based on the golden ratio could be an effective instrument for companies to increase their performance and market acceptance. Strong correlations were discovered between departures from the capital structure based on the golden ratio and the historical maximums of the firms’ sales, market value, income, and stock price. The capital structure based on the golden ratio can be helpful for businesses to improve financial performance [30].

2.5. Hypothesis Development

2.5.1. Debt to Equity (DEEUTY) Ratio

One way to evaluate a business’s use of debt to fund operations is by looking at its DEEUTY ratio. It is calculated by comparing the company’s total debts to its total assets owned by shareholders. The DEEUTY ratio is an important indicator in corporate finance. Financial leverage is the ratio of a company’s reliance on debt financing to its reliance on cash flow from operations [43]. The debt a company owes is compared to the value of its assets minus its liabilities when calculating its DEEUTY ratio. Debt must be repaid or refinanced, and interest expense is incurred. It is usually not deferrable, and the equity value might be reduced or eliminated in the event of a default. Because of this, investors tend to avoid companies with a high DEEUTY ratio, as it indicates a high degree of dependence on debt funding [3]. A corporation with a higher DEEUTY ratio has a higher risk, and a lower DEEUTY ratio is considered a lower risk. The use of debt financing can boost firms’ profitability. Investors stand to gain if earnings exceed the expenses of servicing the debt. However, the share price may decline if the additional cost of debt financing outweighs the additional income it generates. The cost of debt and a company’s ability to service that debt can rise and fall in tandem with the economy [44].

Hypothesis 1 (H1).

Debt-to-equity ratio Deviation from the golden ratio positively influences firms’ financial performance.

2.5.2. Equity (EYTRAT) Ratio

The EYTRAT ratio is a commonly used financial indicator to evaluate a firm’s leverage. It measures the efficiency with which a firm handles its debts and funds its assets needs by looking at the quantity of equity and the amount invested in assets. Companies employing excessive debt to purchase assets are seen as more financially risky [45,46]. The ability to cover asset funding demands with minimal debt is reflected in a lower EYTRAT ratio, which is, in turn, reflected in a higher EYTRAT ratio. For this definition, a corporation is leveraged if its EYTRAT is 0.50 or lower. An increase in a corporation’s EYTRAT ratio leads to a decrease in its use of debt. Firms with an EYTRAT ratio above 0.50 indicate that they rely more on equity financing than debt financing [47]. A corporation can meet its asset funding needs with equity financing and without debt financing. A strong value for the EYTRAT ratio indicates that the corporation is managing its finances well and can meet its debt obligations. The higher the EYTRAT ratio, the stronger the company’s financial health and the more secure its long-term solvency is compared to rival businesses with lower equity ratios. Corporations with lower EYTRAT ratios would not be in a better position to pay off all their debt and have good returns on earnings for other investment activities.

Hypothesis 2 (H2).

The equity ratio’s deviation from the golden ratio positively influences firms’ financial performance.

2.5.3. Capitalization (CAPRAT) Ratio

A company’s CAPRAT ratio can be calculated by dividing its current equity by its total debt. This ratio, also known as the capitalization ratio, measures the proportion of debt to total capital and the proportion of equity utilized to finance business operations. In contrast, a higher CAPRAT ratio indicates that a company has more debt than equity and may be at a higher risk of financial distress [48]. CAPRAT ratios are important for determining a company’s capital structure’s overall debt and equity proportions. A company’s operations can be financed in one of two ways: through debt or equity [49]. When comparing a company’s total debt to its equity, capitalization ratios reveal the degree of financial leverage. A lower CAPRAT ratio is preferable since it indicates that more equity than debt is being used to fund the business. A lower CAPRAT ratio does not necessarily indicate that a company is inferior to those with a higher CAPRAT ratio. The corporation may face less operational risk if it does not use leverage to finance its activities. The company may need more funding to expand in the long run.

Hypothesis 3 (H3).

The capitalization ratio’s deviation from the golden ratio positively influences firms’ financial performance.

2.5.4. Debt to Total to Asset Ratio

A company’s leverage is measured by calculating the LTTTTA ratio, which is the same as the solvency or coverage ratio. Calculating this ratio might give an idea of how much of a company’s assets would have to be sold off to cover the company’s long-term debt. The LTTTTA ratio is defined as total long-term debt as a percentage of total corporate assets. This ratio quantifies the level of financial leverage of a corporation. A corporation can acquire assets with either debt financing or equity financing. When long-term debt exceeds equity, balance sheet ownership falls, and leverage rises, the ratio of LTTTTA grows, showing how heavily a company relies on long-term debt to fund its operations [50,51]. Thus, more assets would have to be liquidated in case of bankruptcy before its debts could be settled. Additionally, the debt repayment would necessitate sustained high sales and cash flow for a considerable period into the future. This ratio can assess a firm’s financial stability and risk profile. Investors should be wary if the ratio is high since it suggests management cannot fund new activities or generate free cash flow. A company’s management often uses this metric to figure out the best way to set up the capital structure and the right amount of debt for the business. Loans with maturities within the next 12 months or the current fiscal year are considered short-term debt. Current liabilities refer to obligations that will need to be paid off quickly. Liabilities incurred within the current accounting period are often settled using assets expected to be consumed within the next 12 months. The ratio of a company’s current assets to its current debts is a major predictor of its ability to satisfy its short-term financial obligations [52,53]. Accounts payable, which represents unpaid invoices to suppliers, is one of the most prominent current liability accounts on a company’s financial statements. Payment dates are coordinated by businesses to ensure that receivables are received ahead of payables to vendors.

Hypothesis 4 (H4).

Short-term debt to total assets ratios that deviate from the golden ratio positively influence firms’ financial performance.

Hypothesis 5 (H5).

Long-term debt to total assets ratios that deviate from the golden ratio positively influence firms’ financial performance.

3. Research Methodology

3.1. Target Population, Sample Size, and Data

The population used for the study was the non-financial institutions in France and the UK. Those two countries were selected based on adopting IFRS to prepare their financial statements. The UK and France have resilient economies that attract more investors worldwide. Apart from having a resilient economy, they are also one of the fastest-growing countries in Europe [54,55]. Establishing a business requires financing, and most investors have issues deciding the percentage of debt and equity to use in their capital structure to finance the business. Moreover, many corporations in the UK and France have not yet established the proportion of debt and equity they can use in their capital structure to have better financial performance and maximize the shareholders’ wealth. The reason for selecting these countries over others was to develop the optimal capital structure that investors seeking to establish businesses in these countries could use to impact their financial performance and maximize shareholder wealth [56].

The data used for the study were from the Thomson Reuter Eikon database. The data used for the study covered 20 years, starting in 2002 and ending in 2021. The companies included those dealing with utilities, consumer cyclical and non-cyclical goods, healthcare, energy, real estate, technology, industrials, and essential materials. Financial institutions were excluded from the study. Financial institutions prepare financial statements in a way that is distinct from how non-financial institutions prepare their financial statements. Combining financial and non-financial institutions would not contribute to achieving the study objectives. The study used 200 non-financial institutions from the UK and 150 from France during 2002–2021. In general, 7000 firm years of observation were used for both countries, of which 4000 firm years of observation were used for the firms in the UK and 3000 firm years of observation were used for France.

Table 1. Firm classifications by their sectors for France and the United Kingdom.

Sectors	No Firms France	No Observations France	Percentage France	No Firms UK	No Observations UK	Percentage UK
Basic Materials	15	300	10%	19	380	9.5%
Consumer Cyclicals	44	880	29.3%	41	820	20.5%
Consumer Non-Cyclicals	16	320	10.7%	25	500	12.5%
Energy	3	60	2%	11	220	5.5%
Industrials	33	660	22%	50	1000	25%
Healthcare	7	140	4.7%	11	220	5.5%
Real Estate	11	220	7.3%	20	400	10%
Technology	20	400	13.3%	16	320	8%
Utilities	1	20	0.7%	7	140	3.5%
Total	150	3000	100%	200	4000	100%

shows sample company classifications according to their sectors in France and the UK.

3.2. Selection of Variables

In this study, five (5) independent variables (DEEUTY, EYTRAT, CAPRAT, STTTTA, and LTTTTA) were used to represent the capital structure; four dependent variables (TOBQ, EPS, ROA, and ROE); and three controlling variables (AGE, IFRS as a dummy variable, and SIZE) were also used. In addition, the golden ratio was applied as (61.8% and 38.2%) to the capital structure. The question is: which of the golden ratios should be used for debt and equity? The average DEEUTY was used for both countries. In France, the DEEUTY was 1.22, and in the UK, it was 1.33. Based on the DEEUTY, the companies in both countries used more debt than equity. Therefore, 61.8% was used to represent debt, and 38.2% was used to represent equity. A positive value obtained after deviation from the golden ratio in debt financing by the firm indicates that the firm uses more debt than the optimal debt requirement of 0.618 in the capital structure. Any negative values obtained after deviation mean that the firms use less debt than the optimal debt requirement of 0.618 in their capital structure. In equity financing by the firms, a positive value obtained after deviation from the golden ratio means the firms are using more equity than the optimal equity requirement of 0.382 in the capital structure. Any negative values obtained after deviation mean that the firms use less equity than the optimal equity requirement of 0.382 in the capital structure. The information on the dependent, independent, and controlling variables is summarized in

Table 2. Description of variables.

Variable	Tape	Description
Tobin’s Q	Dependent	Total market value of firm/total assets of the firm
Earnings per share	Dependent	Net income after tax/total outstanding shar
Return on asset	Dependent	Net income after tax/total assets × 100
Return on equity	Dependent	Net income after tax/total equity × 100
Equity ratio deviation from golden ratio	Independent	(Total equity/total asset) − 0.382
Capitalization ratio deviation from golden ratio	Independent	(Total debt)/(total debt + total equity) − 0.618
Debt to equity deviation from golden ratio	Independent	(Total debt/ total equity) − 0.618
Short term debt to total assets deviation from golden ratio	Independent	(Total current liabilities/total asset) − 0.618
Long term debt to total assets deviation from golden ratio	Independent	(Total long-term liabilities/total asset) − 0.618
IFRS	Dummy	Marked “1” if the firm adopt IFRS, marked “0” if the firm do not adopt IFRS
Firm age	Control	The number of years that the firm has been in the stock market
Size of the firm	Control	Natural log of total asset

.

3.3. Model Specification

This study aimed to determine the impact of a capital structure deviation from the golden ratio on financial performance. Four models were applied in this paper to estimate the effect of capital structure deviation from the golden ratio on financial performance. The models are specified below:

TOBQ = β0 + β1 EYTRAT + β2 CAPRAT + β3 DEEUTY + β4 STTTTA +
β5 LTTTTA + β6 IFRS + β7 AGE + β8SIZE + ℇ

(1)

EPS = β0 + β1 EYTRAT + β2 CAPRAT + β3 DEEUTY + β4 STTTTA +
β5 LTTTTA + β6 IFRS + β7 AGE + β8SIZE + ℇ

(2)

ROA = β0 + β1 EYTRAT + β2 CAPRAT + β3 DEEUTY + β4 STTTTA +
β5 LTTTTA + β6 IFRS + β7 AGE + β8SIZE + ℇ

(3)

ROE = β0 + β1 EYTRAT + β2 CAPRAT + β3 DEEUTY + β4 STTTTA +
β5 LTTTTA + β6 IFRS + β7 AGE + β8SIZE + ℇ

(4)

where Tobin’s Q was denoted as “TOBQ”, earnings per share as “EPS”, return on assets as “ROA”, return on equity as “ROE”, equity ratio deviation from the golden ratio as “EYTRAT”, capitalization ratio deviation from the golden ratio as “CAPRAT”, debt to equity deviation from the golden ratio as “DEEUTY”, short term debt to total assets deviation from the golden ratio as “STTTTA”, long term debt to total assets deviation from the golden ratio as “LTTTTA”, International financial reporting standards as “IFRS”, firm age as “AGE”, the size of the firm as “SIZE” and the error term as “ℇ”.

4. Data Analysis, Results, and Discussions

All the datasets were analyzed using the Stata software. The results include descriptive statistics, a matrix of correlation, diagnostic tests, Panel unit root tests, Sensitivity analysis, and the GMM used to find the effect of the capital structure deviation from the golden ratio on financial performance.

4.1. Descriptive Statistics

Table 3. Descriptive Statistics for France.

Variable	Observations	Mean	Std. Dev.	Min	Max
TOBQ	3000	0.61	0.367	0.206	1.356
EPS	3000	2.868	3.474	−0.238	10.257
ROA	3000	2.766	6.734	−120.392	30.531
ROE	3000	8.872	8.067	−6.244	20.603
EYTRAT	3000	0.015	0.157	−0.499	0.551
CAPRAT	3000	−0.326	0.197	−0.618	0.517
DEEUTY	3000	0.116	0.519	−0.502	1.118
STTTTA	3000	−0.258	0.154	−0.604	0.247
LTTTTA	3000	−0.454	0.126	−0.618	0.361
IFRS	3000	0.85	0.4	0	1
AGE	3000	35.82	18.883	2	158
SIZE	3000	9.098	0.933	5.856	11.154

and

Table 4. Descriptive Statistics for the United Kingdom.

Variable	Observations	Mean	Std. Dev.	Min	Max
TOBQ	3999	0.846	0.551	0.233	1.985
EPS	3999	0.549	0.651	−0.072	1.976
ROA	4000	4.43	4.08	−2.647	10.985
ROE	4000	11.261	11.609	−8.584	31.026
EYTRAT	4000	0.015	0.217	−3.352	0.89
CAPRAT	4000	−0.275	0.741	−29.018	5.727
DEEUTY	4000	0.152	0.59	−0.485	1.395
STTTTA	4000	−0.333	0.17	−0.617	2.317
LTTTTA	4000	−0.389	0.501	−0.618	29.444
IFRS	4000	0.85	0.357	0	1
AGE	4000	44.382	35.253	1	206
SIZE	3999	9.109	0.975	5.084	11.614

present the summary of the descriptive statistics for variables. The average TOBQ for French firms was 0.61, while for the UK, it was 0.846. The firms in the UK have a higher TOBQ than that the firms in France. However, the average TOBQ for both countries indicates that the firms are undervalued since Tobin’s values are less than 1 [57]. The average earnings per share for firms in France was 2.868, while that for firms in the United Kingdom was 0.549. The firms in France have higher earnings per share than those in the UK. The firms in France provide better earnings on their shares than those in the UK. The average ROA recorded by the firms in France was 2.77%, and that in the UK was 4.43%. The firms in the UK earn more on assets than the firms in France. The average ROE of the firms in France was 8.872%, and that of the firms in the UK was 11.261%. Firms in the United Kingdom are more efficient at converting equity financing into profit than those in France.

The average EYTRAT of firms in France that deviated from the golden ratio was 0.15, and firms in the UK were also at 0.15. The firms in the UK and France have the same EYTRAT. The average capitalization ratio that deviated from the golden ratio for the firms in France was −0.326 and −0.275 for the firms in the UK. The CAPRAT deviating from the golden ratio at UK firms is better than that in France. The DEEUTY deviation from the golden ratio for the firm in France was 0.116, and that of the firm in the UK was 0.152. The firms in the UK have better DEEUTY than those in France. The average STTTTA and LTTTTA deviations from the golden ratio of the firms in France were −0.258 and −0.454, respectively, and those of the firms in the UK were −0.333 and −0.389. The firms in France have a better STTTTA ratio than those in the UK. The firms in the UK have better LTTTTA than those in France.

4.2. Matrix of Correlations

Many researchers have used the matrix correlation analysis results to determine multicollinearity [58,59,60]. The strong correlation between two capital structure variables that deviated from the golden ratio variables, which are the independent variables, shows a multicollinearity problem. If the coefficients of two independent variables are greater than 0.70, it shows a problem of multicollinearity [61,62,63]. The matrix correlation analysis results show that the coefficient between two independent variables for both countries is not greater than 0.70. The matrix correlation analysis results show no multicollinearity between our capital structure variables that deviates from the golden ratio.

Table 5. Matrix of correlations for France.

Variables	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
(1) TOBQ	1.000
(2) EPS	0.086	1.000
(3) ROA	0.100	0.024	1.000
(4) ROE	0.238	0.371	0.001	1.000
(5) EYTRAT	0.013	0.048	0.112	0.006	1.000
(6) CAPRAT	0.026	−0.021	−0.117	0.022	−0.624	1.000
(7) DEEUTY	−0.385	−0.052	−0.034	−0.022	0.023	−0.019	1.000
(8) STTTTA	−0.004	−0.036	−0.035	−0.034	−0.574	−0.084	−0.016	1.000
(9) LTTTTA	0.025	0.008	−0.075	0.035	−0.427	0.673	−0.015	−0.397	1.000
(10) IFRS	0.035	0.004	0.010	0.025	0.040	0.027	0.004	−0.089	0.051	1.000
(11) AGE	0.001	0.021	0.022	0.016	0.059	0.022	−0.011	−0.170	0.041	0.212	1.000
(12) SIZE	0.029	−0.057	0.134	0.023	−0.327	0.357	−0.011	−0.070	0.258	0.139	0.192	1.000

and

Table 6. Matrix of correlations for the United Kingdom.

Variables	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
(1) TOBQ	1.000
(2) EPS	−0.015	1.000
(3) ROA	−0.014	0.573	1.000
(4) ROE	0.006	0.524	0.686	1.000
(5) EYTRAT	0.031	0.039	0.098	0.111	1.000
(6) CAPRAT	−0.017	0.018	−0.030	−0.004	−0.124	1.000
(7) DEEUTY	−0.155	−0.006	−0.025	−0.019	0.017	−0.009	1.000
(8) STTTTA	0.006	−0.111	−0.028	0.090	−0.565	−0.065	−0.040	1.000
(9) LTTTTA	0.017	−0.001	−0.064	−0.026	−0.123	0.091	−0.009	−0.092	1.000
(10) IFRS	0.074	0.055	0.000	0.002	0.032	−0.008	0.083	−0.079	−0.001	1.000
(11) AGE	0.006	0.085	0.006	−0.021	0.131	−0.029	0.010	−0.086	−0.033	0.099	1.000
(12) SIZE	−0.000	0.388	0.106	0.202	−0.138	0.145	0.026	−0.163	0.063	0.116	−0.005	1.000

show the matrix correlation between the study variables. The EYTRAT ratios that deviated from the golden ratio for the firms in France and the UK have a positive relationship with TOBQ, EPS, ROA, and ROE. The capitalization ratios of the firms in both countries have a negative relationship with ROA. The DEEUTY ratio deviated from the golden ratio for both firms in France and the UK, which have a negative relationship with TOBQ, EPS, ROA, and ROE. The adoption of IFRS by firms in France and the UK positively correlates with TOBQ, EPS, ROA, and ROE. The firms’ ages in the French stock market positively correlate with TOBQ, EPS, ROA, and ROE. The result is the same as for firms in the UK, except for ROE, which negatively affects. In France, except for EPS, which shows a negative relationship with the size of the firms, TOBQ, ROA, and ROE show a positive relationship with the size of the firms. In the UK, there was a negative relationship between the size of the firms and TOBQ, while the size of the firms also showed a positive relationship with EPS, ROA, and ROE.

4.3. Model Diagnostic Tests

Table 7. Model Diagnostic tests.

	France		UK
Variance inflation factor	VIF	1/VIF	VIF	1/VIF
EYTRAT	2.342	0.653	1.744	0.573
CAPRAT	1.272	0.734	1.057	0.946
DEEUTY	1.113	0.902	1.023	0.978
STTTTA	1.569	0.564	1.702	0.587
LTTTTA	1.452	0.867	1.059	0.944
IFRS	1.062	0.95	1.028	0.973
AGE	1.473	0.681	1.028	0.973
SIZE	1.456	0.345	1.138	0.879
Mean VIF	1.28		1.222	.
Heteroskedasticity Results
Chi-square	118		270.78
p-value	0.441		0.224
Jarque-Bera normality test
Chi-square	377.6		744.7
p-value	0.444		0.511

Notes: VIF, Variance inflation factor.

shows the results of the model diagnostic tests for both France and the UK. Three diagnostic tests were carried out. These include multicollinearity, heteroskedasticity, and normality tests. These assumptions need to be met before the regression model can be computed. In order to check the multicollinearity; the variance inflation factor (VIF) was used. If the VIF results are greater than 10, then there is a problem with multicollinearity [46]. The VIF obtained for France and the UK is less than 10. The results confirmed that there is no problem with multicollinearity. The Breusch pagan white was used to check for the presence of heteroskedasticity, and the null hypothesis for both countries failed to be rejected. The results confirmed that the data are homoscedastic. Moreover, the Jarque Bera was used to check for normality, and the null hypothesis thesis for both countries failed to be rejected. The results also confirmed that the data used for the study were normally distributed.

4.4. Panel Unit Root Tests

Table 8. Panel unit root tests for France (Levin-Lin-Chu unit-root test).

Variables	Statistics (Unadjusted t)	Statistics (Adjusted t *)	p-Value
TOBQ	−37.4117	−30.8842	0.0000
EPS	−31.9189	−25.8361	0.0000
ROA	−38.0033	−31.9187	0.0000
ROE	−38.4796	−32.1793	0.0000
EYTRAT	−36.5057	−31.6321	0.0000
CAPRAT	−38.3724	−32.8766	0.0000
DEEUTY	−40.2174	−35.1034	0.0000
STTTTA	−37.9288	−32.9005	0.0000
LTTTTA	−40.5286	−35.3161	0.0000
AGE	−34.7197	−30.5270	0.0000
SIZE	−31.3288	−30.6001	0.0000

and

Table 9. Panel unit root tests for the United Kingdom (Levin-Lin-Chu unit-root test).

Variables	Statistics (Unadjusted t)	Statistics (Adjusted t *)	p-Value
TOBQ	−45.2282	−42.4775	0.0000
EPS	−42.4437	−35.7358	0.0000
ROA	−47.2882	−42.4975	0.0000
ROE	−45.9498	−40.6362	0.0000
EYTRAT	−43.5707	−36.9379	0.0000
CAPRAT	−44.3497	−38.4566	0.0000
DEEUTY	−45.5836	−40.3556	0.0000
STTTTA	−44.4637	−38.7328	0.0000
LTTTTA	−45.2239	−39.2375	0.0000
AGE	−42.7588	−35.8205	0.0000
SIZE	−42.7588	−35.8205	0.0000

show the results obtained for the panel unit root tests for both France and the United Kingdom. The panel unit root test was computed using the Levin-Lin-Chu. The null hypothesis for the Levin-Lin-Chu shows that the Panels contain unit roots, while the alternative hypothesis shows that the Panels are stationary [64,65]. The Levin-Lin-Chu unit-root test was performed at a level without considering their first difference. The alternative hypothesis for both variables for France and the UK was accepted. The results show that the capital structure variables that deviated from the golden ratio are stationary.

4.5. Dealing with the Problem of Endogeneity

According to Semadeni [66], independent variables used in the regression model must be exogenous. Endogeneity occurred when the independent variables were strongly correlated with the error term [67,68]. Having endogenous variables in the regression model leads to biased estimation, and relying on biased estimation for managerial implications would negatively impact the organization. The literature suggests that using the fixed and random effect models cannot deal with the endogeneity problem and will lead to biased estimation [69,70]. To avoid having biased estimation, many researchers used the general method of movement (GMM) to deal with the problem of endogeneity [71,72,73]. When the past values of the dependent variable influence the current value of an independent variable, this violates the assumption of strict exogeneity in fixed effects estimators and results in dynamic endogeneity [74]. For the exogeneity assumption to hold, the current observations of the independent variables must have no bearing on the past values of the dependent variables [71]. The GMM identified endogenous variables and allowed the use of instrumental variables to deal with the problem by making the variables exogenous. In our study, we applied lag to all the explanatory variables used. One of the ways of dealing with endogeneity is the application of lag to explanatory variables [75,76].

In the GMM model, the Arellano Bond (2) was applied to check for the problem of autocorrelation. The results obtained for all models of this study indicated that there is no autocorrelation. Moreover, the tests of Hansen and Sargant were used to examine the model’s validity. The null hypotheses obtained for the UK and France models failed to be rejected, and the results also showed that the models were valid.

4.6. Dynamic Panel-Data Estimation, Two-Step Difference GMM

Table 10. Dynamic panel-data estimation, two-step difference GMM (France).

Variables	TOBQ		EPS		ROA		ROE
	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value
Lag of TOBQ, EPS, ROA and ROE	0.032 ***	0.000	0.012 ***	0.000	0.234 ***	0.000	−0.096 ***	0.000
	(0.003)		(0.005)		(0.005)		(0.006)
EYTRAT	0.198	0.076	7.438 ***	0.000	37.928 ***	0.000	24.063 ***	0.001
	(0.111)		(1.347)		(1.621)		(5.889)
CAPRAT	1.670 ***	0.000	14.885 ***	0.000	20.870 ***	0.000	18.477 ***	0.004
	(0.117)		(0.891)		(1.143)		(5.069)
DEEUTY	−0.297 ***	0.000	−0.313 ***	0.000	−0.406 ***	0.000	−0.369 ***	0.001
	(0.004)		(0.026)		(0.031)		(0.095)
STTTTA	−0.604 ***	0.000	7.964 ***	0.000	11.570 ***	0.000	24.732 ***	0.000
	(0.102)		(1.153)		(1.427)		(4.006)
LTTTTA	−2.376 ***	0.000	−15.899 ***	0.000	−26.192 ***	0.000	−1.420	0.850
	(0.198)		(1.494)		(1.794)		(7.541)
IFRS	0.036 ***	0.000	1.059 ***	0.000	0.895 ***	0.000	0.890 ***	0.001
	(0.005)		(0.030)		(0.069)		(0.264)
AGE	−0.0005	0.220	0.084 ***	0.000	−0.038 ***	0.000	0.140 ***	0.000
	(0.0004)		(0.004)		(0.006)		(0.015)
SIZE	−0.148 ***	0.000	−6.072 ***	0.000	−2.017 ***	0.000	−8.345 ***	0.000
	(0.027)		(0.116)		(0.327)		(1.007)
Changing GDP	0.0004 ***	0.004	0.032 ***	0.000	0.054 ***	0.000	0.025 ***	0.000
	(0.0001)		(0.001)		(0.001)		(0.004)
Financial crisis	−0.001 ***	0.000	−1.053 ***	0.000	−0.450 ***	0.000	−1.789 ***	0.000
	(0.060)		(0.023)		(0.041)		(0.172)
N. of observations	2700		2700		2700		2700
AR (1)	0.000		0.004		0.000		0.003
AR (2)	0.735		0.639		0.345		0.563
Sargan test	0.567		0.456		0.234		0.123
Hansen test	0.234		0.123		0.146		0.291

Notes: The superscript *** p < 0.01, denote statistical significance at the 1% levels, respectively; GDP, Changing in the gross domestic product; Financial crisis 2008.

and

Table 11. Dynamic panel-data estimation, two-step difference GMM (United Kingdom).

Variables	TOBQ		EPS		ROA		ROE
	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value
Lag of TOBQ, EPS, ROA and ROE	0.043 ***	0.000	0.164 ***	0.000	0.141 ***	0.000	0.166 ***	0.000
	(0.002)		(0.012)		(0.015)		(0.016)
EYTRAT	0.840 ***	0.000	1.761 ***	0.000	21.312 ***	0.000	39.847 ***	0.000
	(0.064)		(0.061)		(0.763)		(2.949)
CAPRAT	−0.032 ***	0.000	−0.038 ***	0.000	−0.060 ***	0.161	−0.902 ***	0.000
	(0.003)		(0.004)		(0.043)		(0.110)
DEEUTY	−0.130 ***	0.000	−0.014 ***	0.000	−0.207 ***	0.000	−0.537 ***	0.000
	(0.003)		(0.002)		(0.035)		(0.087)
STTTTA	−1.311 ***	0.000	0.520 ***	0.000	6.441 ***	0.000	18.930 ***	0.000
	(0.086)		(0.062)		(0.715)		(2.577)
LTTTTA	−0.075 ***	0.000	0.020	0.260	−0.318 **	0.051	1.558	0.170
	(.017)		(0.017)		(0.162)		(1.131)
IFRS	0.015 **	0.056	0.071 ***	0.000	1.043 ***	0.000	3.193 ***	0.001
	(0.007)		(0.009)		(0.103)		(0.234)
AGE	0.007 ***	0.000	−0.018 ***	0.000	−0.096 ***	0.000	−0.322 ***	0.000
	(0.0008)		(0.001)		(0.008)		(0.034)
SIZE	−0.532 ***	0.000	0.444 ***	0.000	−1.970 ***	0.000	−5.063 ***	0.001
	(0.040)		(0.047)		(0.345)		(1.276)
Changing GDP	−0.005 ***	0.000	−0.001 ***	0.000	−0.009 ***	0.001	−0.030 ***	0.000
	(0.0001)		(0.0001)		(0.002)		(0.006)
Financial crisis	−0.078 ***	0.000	−0.163 ***	0.000	−1.569 ***	0.000	−4.239 ***	0.000
	(0.005)		(0.006)		(0.084)		(0.251)
N. of observations	3596		3596		3596		3596
AR (1)	0.002		0.000		0.000		0.005
AR (2)	0.235		0.467		0.672		0.782
Sargan test	0.123		0.453		0.873		0.234
Hansen test	0.345		0.237		0.201		0.129

Notes: The superscript *** p < 0.01, ** p < 0.05 denote statistical significance at the 1%, 5% levels, respectively; GDP, Changing in the gross domestic product; Financial crisis 2008.

show the GMM results obtained for the firms in both France and the United Kingdom.

4.6.1. The Impact of a Golden Ratio-Based Capital Structure on Tobin’s Q

In the result of this study, it can be concluded that the dynamic panel has a positive and significant impact on the TOBQ of the firms in France and the UK. Moreover, the EYTRAT deviation from the golden ratio had a positive impact on TOBQ in the French firms and a positive and significant impact on TOBQ in the UK firms. If the firms of both countries increase the practice of equity in their capital structures by 1%, TOBQ in those countries will also increase by 0.19% and 0.84%, respectively. It was also found that the CAPRAT ratio deviating from the golden ratio of the firms in France has a positive and significant impact on TOBQ. The positive impact of the CAPRAT ratio deviating from the golden ratio by the firms in France supports the net income approach to capital structure theory by Durand [77], which says that a larger capital structure with a lower weighted average cost of capital (WACC) is associated with a higher market value for a company that uses debt to finance its investments.

In the UK, the CAPRAT ratio deviated from the golden ratio of the firms can have a negative and statistically significant impact on TOBQ, as shown in the results. It was discovered that deviations from the golden ratio in the DEEUTY ratio, STTTTA ratio, and LTTTTA ratio had a negative and statistically significant impact on TOBQ in both countries. The negative effect of the DEEUTY ratio on the TOBQ of the firms in both countries is consistent with the findings of earlier research [78,79]. The effect of STTTTA and LTTTTA on TOBQ was in line with the finding of Ahmad & Afza [80]. The adoption of IFRS by firms in both countries has a positive and statistically significant impact on TOBQ. In this work, it is revealed that GDP growth in France firms has a positive and significant impact on TOBQ. In contrast, in the UK, it has a negative and significant impact on firms’ TOBQ. It is determined that the 2008 financial crisis had a negative and significant impact on TOBQ for the firms in both countries.

4.6.2. The Impact of a Golden Ratio-Based Capital Structure on EPS

In this study, it is found that the dynamic panel has a positive and significant impact on the EPS of the firms in both countries. The EYTRAT ratio deviates from the golden ratio and has a positive and statistically significant impact on both firms’ EPS in France and the UK. In France, the CAPRAT ratio of the firms that deviated from the golden ratio had a positive and statistically significant impact on EPS, and different results for the firms in the UK were obtained. The positive and significant impact of the CAPRAT ratio on the firms in France is consistent with the finding of a prior study [81]. In the UK, the result of this work showed that CAPRAT ratios that deviated from the golden ratio had a negative and significant impact on firms’ EPS. In both countries, it is achieved in this study that the DEEUTY ratio that deviated from the golden ratio had a negative and significant impact on EPS. In addition, STTTTA deviated from the golden ratio at the firms in France and the UK observed, and it had a positive and significant impact on EPS. The positive effect of STTTTA deviating from the golden ratio on EPS by the firms in both countries supports the claim in Proposition II that leverage improves a company’s value and lowers its weighted average cost of capital [82].

The adoption of IFRS by firms in both countries has a positive and statistically significant impact on EPS. In The result of this study, it is found that the 2008 financial crisis had a negative and significant impact on EPS for the firms in both countries.

4.6.3. The Impact of A Golden Ratio-Based Capital Structure on ROA

In both countries, the study found that the dynamic panel has a positive and statistically significant impact on the ROA of the firms. The EYTRAT and STTTTA that deviated from the golden ratio by the firms in both countries had a positive and significant impact on ROA. The deviation of the EYTRAT ratio from the golden ratio can have a positive impact on ROA contradicts the findings of Vătavu [83], who found a negative impact of the equity ratio on ROA. However, the positive impact of STTTTA is consistent with the findings of a study conducted in Nigeria [78].

In France, the CAPRAT ratio was seen to have a positive and statistically significant impact on the ROA of the firms, and the results are the same as the findings obtained from a Turkish study [24]. In both countries, the results showed that the DEEUTY ratio and LTTTTA that deviated from the golden ratio had a negative and significant impact on ROA, and the results are consistent with the findings obtained by the following researchers [84,85,86]. The adoption of IFRS by firms in both countries has a positive and statistically significant impact on ROA, and the findings match the results obtained by Abdullah & Tursoy [27]. In France, the country’s GDP growth has a positive and significant impact on ROA. The growth of the UK’s GDP has a negative and significant impact on ROA. In both countries, the 2008 financial crisis year had a negative and significant impact on the firms’ ROA.

The positive impact of the CAPRAT ratio and STTTTA, which deviated from the golden ratio, supports the traditional capital structure theory. According to traditional capital structure theory, an optimal capital structure exists whenever the weighted average cost of capital (WACC) is minimized and the market value of assets is maximized [87]. In order to accomplish this, a combination of equity and debt financing is used. There is an opportunity to increase firm value by increasing or decreasing leverage until the marginal cost of debt and the marginal cost of equity are equal.

4.6.4. The Impact of Golden Ratio-Based Capital Structure on ROE

In France, the study found that the dynamic panel has a negative and statistically significant impact on the ROE of the firms. In the UK, it was examined that the dynamic panel has a positive and significant impact on the firms’ ROE. The EYTRAT ratio and STTTTA that deviated from the golden ratio by the firms in both countries had a positive and significant impact on ROE. In France, the CAPRAT ratio deviated from the golden ratio and was seen to have a positive and statistically significant impact on the ROE of the firms. The results obtained for the firms in France differ from those obtained for the UK firms. In the UK, it was determined that the CAPRAT ratio of firms that deviated from the golden ratio had a negative impact on ROE, and the results are consistent with the findings of a prior study [81]. In both countries, the study found that the DEEUTY ratio that deviated from the golden ratio had a negative and significant impact on ROE, and the results are consistent with the findings of earlier research [88]. In France, we found that LTTTTA, which deviates from the golden ratio, has a negative impact on ROE, while in the UK, it has a positive impact on ROE. The positive impact of the firms in the UK deviating from the golden ratio in terms of LTTTTA is consistent with the findings of previous studies [89,90]. The adoption of IFRS by firms in both countries has a positive and statistically significant impact on ROE. In France, the country’s GDP growth has a positive and significant impact on ROE. The growth of the UK’s GDP has a negative and significant impact on ROE. In both countries, the 2008 financial crisis year had a negative and significant impact on the firms’ ROE. Other researches also confirm the importance of performance as a sustainable way of measuring service quality, as they have used new trending approaches in different social and scientific fields to analyze and enhance the quality of performance, and the quality of service has also been utilized to assess service performance and social competence [91,92,93].

4.7. Sensitivity Analysis

Table 12. Sensitivity analysis for France.

Variables	TOBQ		EPS		ROA		ROE
	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value
EYTRAT	0.061	0.641	1.2	0.371	13.355 ***	0.000	1.639	0.601
	(0.131)		(1.193)		(2.508)		(3.136)
CAPRAT	0.008	0.947	−1.32	0.269	−10.985 ***	0.000	−0.855	0.76
	(0.117)		(1.193)		(2.233)		(2.793)
DEEUTY	−0.273 ***	0.000	−0.302 **	0.013	−0.508 **	0.027	−0.233	0.416
	(0.012)		(0.122)		(0.229)		(0.287)
STTTTA	0.043	0.695	0.729	0.519	12.729 ***	0.000	0.874	0.741
	(0.111)		(1.131)		(2.115)		(2.645)
LTTTTA	0.062	0.712	3.003	0.079	21.769 ***	0.000	4.24	0.289
	(0.168)		(1.712)		(3.201)		(4.002)
IFRS	0.024	0.529	0.045	0.848	0.23	0.666	0.329	0.679
	(0.038)		(0.234)		(0.533)		(0.795)
AGE	−0.029	0.479	0.003	0.492	0.013 *	0.098	−0.01	0.34
	(041)		(0.004)		(0.008)		(0.01)
SIZE	0.008	0.334	−0.134	0.105	1.873 ***	0.000	0.252	0.193
	(0.008)		(0.083)		(0.155)		(0.193)
Changing GDP	0.007	0.187	0.018	0.553	0.202 ***	0.004	0.039	0.714
	(0.005)		(0.031)		(0.07)		(0.105)
Financial crisis	−0.002	0.975	−0.735 *	0.075	−0.135	0.886	−1.142	0.419
	(0.067)		(0.412)		(0.943)		(1.414)
Basic Materials	0.012	0.897	−0.87	0.353	3.976 **	0.023	−5.18 **	0.018
	(0.092)		(0.937)		(1.754)		(2.195)
Consumer Cyclical	0.049	0.58	176.	0.847	3.495 **	0.04	−5.188 **	0.015
	(0.089)		(0.911)		(1.705)		(2.133)
Consumer Noncyclical	0.068	0.46	−0.819	0.383	5.556 ***	0.002	−4.123 *	0.061
	(0.092)		(0.939)		(1.759)		(2.2)
Energy	−0.036	0.72	0.644	0.534	3.39 *	0.08	−4.824 **	.047
	(0.102)		(1.036)		(1.939)		(2.425)
Healthcare	0.089	0.344	−0.175	0.855	3.573 **	0.047	−4.892 **	0.029
	(0.094)		(0.959)		(1.795)		(2.245)
Industrials	0.037	0.679	0.19	0.834	3.751 **	0.027	−4.081 *	0.055
	(0.089)		(0.908)		(1.699)		(2.125)
Real-estate	0.003	0.975	0.362	0.699	3.216 *	0.066	−4.415 **	0.044
	(0.092)		(0.934)		(1.749)		(2.188)
Technology	0.06	0.504	−0.459	0.617	4.91 ***	0.004	−4.849 **	0.024
	(0.09)		(0.919)		(1.721)		(2.152)
Constant	0.555 ***	0.000	5.205 ***	0.000	−8.916 ***	0.000	13.12 ***	0.000
	(0.128)		(1.283)		(2.414)		(3.343)
N. of observations	3000		3000		3000		3000
R-square	0.371		0.280		0.365		0.125
F-test	534.503 ***		81.914 ***		276.514 ***		22.529 ***
	(0.000)		(0.000)		(0.000)		(0.000)
Hausman specification tests (p-value)	0.874		0.581		0.619		0.821

Notes: The superscript *** p < 0.01, ** p < 0.05, and * p < 0.1 denote statistical significance at the 1%, 5%, and 10% levels, respectively.

and

Table 13. Sensitivity analysis for the United Kingdom.

Variables	TOBQ		EPS		ROA		ROE
	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value	Coefficient (Std. Dev.)	p-Value
EYTRAT	−0.125 **	0.016	0.227 ***	0.000	2.783 ***	0.000	−1.594	0.14
	(0.052)		(0.057)		(0.384)		(3.109)
CAPRAT	−0.019	0.103	−0.02	0.131	0.057	0.508	−0.453 *	0.062
	(0.012)		(0.013)		(0.086)		(2.776)
DEEUTY	−0.152 ***	0.000	−0.009	0.569	−0.177 *	0.098	−0.348	0.248
	(0.015)		(0.016)		(0.107)		(0.286)
STTTTA	−0.11 *	0.096	−0.004	0.961	1.69 ***	0.001	6.845 ***	0.000
	(0.066)		(0.073)		(0.488)		(2.635)
LTTTTA	0.012	0.504	−0.007	0.734	−0.347 ***	0.007	−0.659 *	0.068
	(0.017)		(0.019)		(0.128)		(3.972)
IFRS	0.091	0.244	0.003	0.941	0.081	0.799	0.478	0.57
	(0.078)		(0.037)		(0.319)		(0.708)
AGE	0.025	0.308	0.001 ***	0.000	0.041	0.818	0.002	0.673
	(0.027)		(0)		(0.181)		(0.008)
SIZE	−0.001	0.926	0.274 ***	0.000	0.619 ***	0.000	2.736 ***	0.000
	(0.009)		(0.01)		(0.069)		(0.19)
Changing GDP	−0.004	0.295	−0.001	0.694	−0.008	0.626	−0.04	0.377
	(0.004)		(0.002)		(0.017)		(3.109)
Financial crisis	−0.063	0.622	−0.121 **	0.041	−1.346 ***	0.01	−2.727 **	0.377
	(0.128)		(0.06)		(0.521)		(2.776)
Basic Materials	−0.032	0.547	−0.094	0.114	−0.583	0.14	−2.759 **	0.013
	(0.054)		(0.059)		(0.395)		(0.286)
Consumer Cyclical	−0.072	0.142	−0.07	0.197	−0.557	0.125	−2.667 ***	0.009
	(0.049)		(0.054)		(0.363)		(2.635)
Consumer Noncyclical	−0.03	0.561	−0.051	0.368	0.01	0.98	−1.195	0.265
	(0.052)		(0.057)		(0.381)		(3.972)
Energy	0.053	0.363	−0.044	0.995	−0.731 *	0.089	−2.043 *	0.091
	(0.058)		(0.065)		(0.431)		(0.708)
Healthcare	−0.038	0.524	−0.254 ***	0.000	−0.308	0.48	−1.264	0.032
	(0.059)		(0.065)		(0.436)		(0.008)
Industrials	−0.036	0.458	−0.125 **	0.021	−0.501	0.164	−2.756 ***	0.006
	(0.049)		(0.054)		(0.359)		(0.19)
Real-estate	−0.009	0.859	−0.165 ***	0.005	−1.024 ***	0.009	−3.463 ***	0.002
	(0.053)		(0.058)		(0.39)		(0.19)
Technology	−0.009	0.864	−0.28 ***	0.000	−1.571 ***	0.000	−4.208 ***	0.000
	(0.054)		(0.06)		(0.401)		(0.19)
Constant	0.946 ***	0.000	−1.896 ***	0.000	−0.091	0.905	−8.746 ***	0.000
	(0.119)		(0.11)		(0.761)		(2.077)
N. of observations	3998		3998		3999		3999
R-square	0.360		0.183		0.478	0.694
F-test	133.856 ***		880.755 ***		186.019 ***		302.614 ***
	(0.000)		(0.000)		(0.000)		(0.000)
Hausman specification tests (p-value)	0.798		0.672		0.478		0.625

Notes: The superscript *** p < 0.01, ** p < 0.05, and * p < 0.1 denote statistical significance at the 1%, 5%, and 10% levels, respectively.

show the results obtained for our sensitivity analysis for the firms in France and the United Kingdom. The sensitivity analysis was conducted to check the robustness of the finding by using the random effect. GDP growth, the 2008 financial crisis, and industry variables were added to our regression model. The results from Table 12 and Table 13 are robust compared to the findings. The findings of this work showed that the 2008 financial crisis had a negative impact on TOBQ, EPS, ROA, and ROE in both countries. In France, it was observed that GDP growth had a positive impact on the firms. In the UK, the study found that GDP growth had a negative impact on the TOBQ, EPS, ROA, and ROE of the firms. Similarly, F-tests for all four models for both firms in France and the UK are statistically significant. The F-tests show that the golden ratio capital structure (EYTRAT, CAPRAT, DEEUTY, STTTTA, and LTTTTA) jointly affects financial performance.

5. Conclusions

The proper selection of debt and equity contributes to higher financial performance. Firms prefer using debt to equity due to the benefits of debt financing. The greater percentage of debt also diluted the ownership and control of shareholders. The use of debt is cheaper than the use of equity. The use of debt involves the fixed payment of interest, while the use of equity involves the payment of dividends to shareholders, which are not fixed but based on the earnings declared by the corporation. Therefore, properly selecting debt and equity in the capital structure led to higher and better financial performance. The pecking order theory suggests that firms should use internally generated funding first, followed by debt and equity. In using debt and equity, the percentage of debt and equity should be used as it is not specified in the literature.

For this reason, the study applies the golden ratio as an optimal capital structure to find the effect of a golden ratio-based capital structure on financial performance using firms from the U.K. and French stock markets. This paper chose a purposive sampling technique to obtain 200 firms in the U.K. and 150 firms in France. The data from all selected companies from 2002 to 2021 was selected and used. The general method of movement (GMM) was applied to estimate the impact of the golden ratio of the firm’s capital structure on financial performance. The golden ratio to the capital structure of the firms has been examined. It is assumed that the firm’s debt and equity percentages used in the capital structure should be 0.618 and 0.382, respectively.

From the results of this study, it can be concluded that when a firm uses EYTRAT at a percentage of 38.2% in the capital structure, it can positively and significantly impact the financial performance of France and the U.K. However, this paper found that the DEEUTY ratio, which deviates from the golden ratio for both firms in France and the U.K., has a negative and significant impact on TOBQ, EPS, ROA, and ROE. When the firms used debt to the tune of 0.618, it had a negative impact on their financial performance. In France, the CAPRAT ratio that deviates from the golden ratio has a positive and significant impact on TOBQ, EPS, ROA, and ROE. In the U.K., the CAPRAT ratio that deviated from the golden ratio had a negative and statistically significant impact on TOBQ, EPS, ROA, and ROE. In France, it was found that LTTTTA that deviated from the golden ratio had a negative and statistically significant impact on TOBQ, EPS, ROA, and ROE. However, this research determined that LTTTTA that deviated from the golden ratio had a negative impact on TOBQ and ROA in the U.K. It is also concluded that adopting IFRS by both firms in the two countries had a positive and significant impact on TOBQ, EPS, ROA, and ROE. The study found that the 2008 financial crisis had a negative and significant impact on TOBQ, EPS, ROA, and ROE.

The study contributes to the literature by investigating the effect of golden-ratio-based capital structure deviance on financial performance using a sample of non-financial institutions from France and the U.K. The study also contributes to the literature by finding that the effect of capital structure (EYTRAT, CAPRAT, DEEUTY, STTTTA, and LTTTTA) deviates from the golden ratio on financial performance (TOBQ, EPS, ROA, and ROE).

5.1. Implication for A Manager

The literature has yet to specify the percentage of debt and equity that firms should use in their capital structure to maximize their value and impact their financial performance. Most arguments have been that corporations should use 70% debt and 30% equity or 50% debt and 50% equity. This research was carried out to help managers realize the optimal percentage of debt and equity that should be used in the capital structure to maximize the corporation’s wealth and improve the corporation’s financial performance in the UK and France.

In France, the result of the study displayed that when managers chose an EYTRAT percentage of 38.2%, it had a positive impact on TOBQ, EPS, ROA, and ROE. For managers to decide the percentage of equity that can be used in their capital structure, they should consider using an optimal equity level of 38.2%, which leads to better financial performance. When managers decide the percentage of the debt component that should be included in the CAPRAT ratio that will give them better financial performance, they should use an optimal debt component of 61.8%. When managers consider the optimal percentage of the debt component for their DEEUTY ratio, using debt up to 61.8% would lead to poor financial performance. They should therefore consider using debt below 61.8% when determining the optimal percentage of debt to be used in the debt-to-equity ratio. When an optimal debt of 61.8% is used as an STTTTA in the capital structure to finance the business, it leads to better financial performance. However, when an optimal debt of 61.8% is used as LTTTTA in the capital structure to finance the business’s assets, it leads to poor financial performance.

In the United Kingdom, it can be concluded that when managers chose an EYTRAT percentage of 38.2%, it had a positive impact on TOBQ, EPS, ROA, and ROE. For managers to decide the percentage of equity that can be used in their capital, they should consider using an optimal equity level of 38.2%, which leads to better financial performance. When managers decide the percentage of the debt component that should be included in their CAPRAT that will lead to poor financial performance, they should not use an optimal debt component of 61.8%. When they use debt at 61.8%, it will lead to poor financial performance. When managers consider the optimal percentage of the debt component for their DEEUTY ratio, using debt up to 61.8% would lead to poor financial performance. They should therefore consider using debt below 61.8% when determining the optimal percentage of debt to be used in the DEEUTY ratio. When an optimal debt component of 61.8% is used as STTTTA in the capital structure to finance the business, it leads to better financial performance.

5.2. Limitations, Recommendations, and Future Research Direction

The study is limited to firms in the U.K. and French stock markets, and the findings may not be generalizable to other markets. Additionally, the study assumes that the firm’s debt and equity percentages used in the capital structure should be 0.618 and 0.382, respectively, based on the golden ratio, which may not hold for all firms. Another limitation of the study was that there were a limited number of studies performed by applying the golden ratio to the firms’ capital structure, which made it difficult to compare our results to existing findings. There have been many studies on the impact of capital structure on financial performance, but more attention should be given to the golden ratio deviation in capital structure. Many capital structure variables were not part of the model. These include the total debt-to-capitalization ratio, total debt-to-assets ratio, and short-term debt-to-capitalization ratio; therefore, researchers considering applying the golden ratio to capital structures in the future should focus on the aforementioned variables to contribute significantly to the literature. Moreover, not only can the golden ratio be applied to the capital structure, but future studies should consider applying it to dividend policy and earnings management. The future study can also make a comparison between the golden ratio, which assumes 61.8% debt and 38.2% equity, the use of 30% equity and 70% debt, and the use of 50% debt and 50% equity, which one contributes to higher profitability of the firm in the various sectors of the business environment.