Open AccessArticle

Bankruptcy Prediction for Restaurant Firms: A Comparative Analysis of Multiple Discriminant Analysis and Logistic Regression

Yang Huo

¹,

Leo H. Chan

^2,*

and

Doug Miller

Department of Strategy Management and Operations, Utah Valley University, Orem, UT 84058, USA

Department of Finance and Economics, Utah Valley University, Orem, UT 84058, USA

Author to whom correspondence should be addressed.

J. Risk Financial Manag. 2024, 17(9), 399; https://doi.org/10.3390/jrfm17090399

Submission received: 27 July 2024 / Revised: 20 August 2024 / Accepted: 4 September 2024 / Published: 6 September 2024

(This article belongs to the Special Issue Advances in Financial and Hospitality Management Accounting)

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Abstract

In this paper, we used data from publicly traded restaurant firms between 2000 and 2019 to test the effectiveness of multiple discriminant analysis (MDA) and logistic regression (logit) in predicting the probability of bankruptcy in the restaurant industry. We constructed various financial ratios extracted from the financial information and analyzed them to determine the optimal models. Our results show that liquid ratios (particularly the quick ratio), operating cash flow, and working capital emerge as the most crucial indicators of potential bankruptcy filings for restaurant firms. The results also show that the logit model performs better within the sample. However, both models exhibit similar predictive capacities with out-of-sample data.

Keywords:

bankruptcy prediction model; financial ratios; business failure; logistic regression; multidiscriminant analysis

1. Introduction

There has been a sharp increase in bankruptcy rates among U.S. companies since the beginning of 2023. The total number of business bankruptcies filed in the calendar year ending 30 June 2023 amounted to 15,724, rising 23.3 percent from 12,748 in 2022 (Administrative Office of the Courts 2023). Sabater and Longoria (2024) report that U.S. corporate bankruptcy filing reached the highest monthly rate since the onset of the COVID-19 pandemic. The reasons behind these failures are multifaceted, including external environmental factors such as COVID-19-related restrictions, government regulations, economic challenges, intense market competition, and shifts in consumer behavior. Internal factors such as operational or capital structures also play vital roles. Of all the internal factors, the degree of financial and operating leverage is the most crucial determinant of bankruptcy risk, as it amplifies operating losses in challenging market conditions.

The restaurant industry is known for its high fixed cost, high labor turnover, low operating margin, and highly cyclical against the business cycle. Any minor disruption in the supply and demand related to their operation could lead to business failures. The social distancing practices during the height of the COVID-19 pandemic caused disruptions in both supply and demand to their operating environment that have never been seen since the Great Depression. The lockdown practices not only limited the operation of the restaurant industry but those practices also reduced the demand for lunch services as most office workers were working from home. As a result, employment in leisure and hospitality plummeted by 459,000, primarily in food services and drinking businesses (BLS 2020), within months of the onset of the pandemic. In the ensuing two years after the onset of the pandemic, the restaurant industry suffered a higher-than-usual rate of bankruptcies.

By the end of 2021, when authorities lifted most COVID-19-related restrictions, we saw a significant increase in demand for the hospitality and food service industry and a substantial decline in the labor supply. Furthermore, the supply chain disruptions also drove up the cost of most inputs. These two factors combined led to many small, locally-owned restaurants closing. LendingTree analysis of BLS data (2022) indicates that the restaurant industry experienced the highest 1-year business failure rate, 19%, among all segments in the retail trade sector. While larger restaurant chains have more capital and ways to raise funds to support a short-term disruption that causes declines in operating results, these larger firms cannot sustain longer-term challenges to their operation. Since the start of 2023, a few high-profile restaurant chains have filed for Chapter 11 or Chapter 7 bankruptcy (Coley 2023; Ruggless 2023; Hauari and Sims 2024).

Moreover, the higher interest rates imposed by the Fed to fight inflation (mainly to reduce demand) created many uncertainties for the service industry. There is a looming expectation of a mild recession that could result in increased bankruptcy filings for highly leveraged independent restaurants, chain-affiliated restaurants, and even franchised units in the coming years. The ability to predict business failure becomes even more critical for the survival of the restaurant industry in the current challenging economic conditions. Altman (2024) argues that we are only at the beginning of the distressed level of the credit cycle, and more business failures will likely happen throughout the credit cycle. If predictive models can be used to predict the likelihood of restaurant failure or bankruptcy, owners and operators can proactively address those issues before they escalate to a point of no return. This study aims to discuss the pros and cons of current bankruptcy prediction models and determine the main factors that lead to bankruptcy in the restaurant industry. By doing so, we hope the findings of this paper can be used as a tool for restaurant operators to spot signs of financial troubles ahead so that they can avoid the bankruptcy route.

We used data from publicly traded restaurant firms between 2000 and 2019 to test the predictability of bankruptcy in the restaurant industry using multiple discriminant analysis (MDA) and logistic regression (logit). We constructed various financial ratios extracted from the financial information and analyzed them to determine the optimal models. Our results show that liquid ratios (particularly the quick ratio), operating cash flow, and working capital emerge as the most crucial indicators. The results also show that the logit model performs better within the sample. However, both models exhibit similar predictive capacities with out-of-sample data. Our study contributes to the existing literature in two ways: First, we utilized a longer horizon data window that covers observations up to the year before the onset of the pandemic. Second, we have the most comprehensive dataset for publicly traded restaurant firms compared to previous studies of bankruptcy in the restaurant industry.

We organize this paper as follows: Section 2 provides a concise overview of the evolution of bankruptcy prediction models as a tool for assessing a company’s financial performance. Section 3 details the research methodology, discussing sampling and data collection methods and emphasizing their relevance to ratio analysis in the context of bankruptcy prediction. Section 4 presents the findings and results of the bankruptcy prediction models. Section 5 concludes the paper by highlighting the potential value of our findings for restaurant firms facing operational and financial challenges and offering suggestions for further research.

2. Literature Review

2.1. Evolution of Bankruptcy Prediction Models and Multivariate Discriminant Analysis

Since the work of Altman (1968), the issue of business failure and bankruptcy prediction has garnered significant attention in academic literature for many decades. A growing body of research on business failure (Carter and Auken 2006; Cepec and Grajzl 2020; Clark et al. 1997; Darayseh et al. 2003; Grice and Dugan 2001; Hahnenstein and Röder 2003; Khan 1985; Lukason and Hoffman 2014; Nishikawa 2002; Onakoya and Olotu 2017; Morris 1997; Tan and Dihardjo 2001; White 2016) indicates that many firms have encountered some common financial challenges (as indicated by financial ratios) that eventually lead to bankruptcy. The ability to identify leading financial indicators that would lead a company to file for bankruptcy can assist executives in adjusting their operational and financial decision making to prevent the firm from going down the path of bankruptcy. Even for financially healthy companies, the ability to accurately predict the probability of bankruptcy could guide the company in formulating the best operational and financial decision strategy to benefit all stakeholders

Researchers have widely used the multivariate discriminant analysis (MDA) bankruptcy prediction model that Altman (1968) developed to predict business failure. They extensively apply MDA in situations where the primary objective is to identify the group to which an object belongs (Hair et al. 2019). The function model estimates the relationship between a single nonmetric (categorical or nominal ratio) dependent variable and a set of metric independent variables.

Altman’s initial model used 22 financial ratios from 66 manufacturing companies (33 failed and 33 successful). All ratios were tested for their significance and discarded if their significance failed to meet certain thresholds. The final model has five ratios:

Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 0.999X5

where

X1 = Working Capital/Total Assets;
X2 = Retained Earnings/Total Assets;
X3 = EBIT/Total Assets;
X4 = MKT. Value Equity/Total Debt;
X5 = Sales/Total Assets.

Firms with a Z score above 2.99 fall into the “nonbankrupt” sector, while those with a Z score below 1.81 are in the “bankrupt” sector. The area between 1.81 and 2.99 is the “zone of ignorance” due to potential classification errors (Altman 1968).

Fulmer et al. (1984) suggested modifications, eliminating the Sales/Total Assets ratio. The corrected model expresses four ratios as follows:

Zjk = 6.56X1 + 3.26X2 + 6.72X3 + 1.05X4

The predetermined cutoffs for the Z score are

The firm fails when Z < 1.1;
The zone of ignorance is between 1.1 and 2.6;
The firm does not fail when Z > 2.6.

Bellovary et al. (2007) studied the evolution of bankruptcy prediction models from 1930 to 2007, finding that MDA and neural networks are promising methods. They concluded that the number of factors (ratios) associated with bankruptcy prediction is not crucial; models with 2 factors can predict as accurately as those with 21 factors.

While many studies focus on bankruptcy prediction in the manufacturing industry, Adams (1991) applied Altman’s MDA model to the U.K. leisure and lodging industry, emphasizing its importance for predicting business failure in different asset structures, operating conditions, and financing requirements within the service sector, including the restaurant industry.

2.2. Logistic Regression

A popular alternative to the MDA model is the logistic regression. Logistic regression estimates the probability of an event, such as success or failure, based on a given dataset of independent variables. Since the outcome is a probability, the dependent variable ranges between 0 and 1. In logistic regression, we apply a logit transformation to the odds, which are the ratio of the probability of success to the probability of failure or vice versa. We commonly refer to this transformation as the log odds, and we call the log of the odds ratio the logit. The transformed model is linear in the beta (β) coefficients, or the natural logarithm of odds. The following formulas represent the logistic function:

Logit (pi) = 1/(1 + exp(−pi))

ln(pi/(1 − pi)) = Beta_0 + Beta_1 × X_1 + … + B_k × K_k

Logit (pi) represents this logistic regression equation’s dependent or response variable, and x denotes the independent variable. This model’s beta parameter or coefficient is commonly estimated through maximum likelihood estimation (MLE). MLE tests various beta values through multiple iterations to optimize the best fit of log odds. These iterations produce the log-likelihood function, and logistic regression aims to maximize this function to determine the optimal parameter estimate. After identifying the optimal coefficient (or coefficients if there are multiple independent variables), we calculate, log, and sum the conditional probabilities for each observation to yield a predicted probability. For binary classification, a probability less than 0.5 predicts 0, while a probability greater than 0 predicts 1. After computing the model, it is advisable to assess its goodness of fit, which is how well it predicts the dependent variable. The Hosmer–Lemeshow test is a popular method for evaluating model fit.

Hair et al. (2019) assert that logistic regression is less affected by variables’ normality than discriminant analysis. They highlight its usefulness when the primary goal is identifying the firm to which a dependent binary nonmetric variable belongs (e.g., success or failure). At the same time, discriminant analysis is more suitable when dealing with three or more groups forming the dependent variable.

Machine Learning Models

Applying machine learning (ML) models in business research studies has been increasingly popular in recent years (see Becerra-Vicario et al. 2020; Kim and Upneja 2014; Siswoyo et al. 2022). Simple models like the logit model have been incorporated into the ML toolkits. While more complex ML models could discover hidden features that traditional theory-based models might not be able to detect, there is a trade-off between model complexity and interpretability of various ML models. In cases where the available data are limited, ML models tend to overfit, leading to questionable results. It is beyond the scope of this paper to compare the efficacy of various ML models compared to logit and MDA analysis. Researchers interested in this topic should consult the most current ML application literatures and know the trade-offs between ML models and traditional statistical models.

2.3. Bankruptcy Prediction Studies in the Hospitality and Service Industry

Based on the review of the bankruptcy prediction models outlined in the previous sections and building upon previous research on restaurant firm bankruptcy prediction models (Barreda et al. 2017; Gu 2002; Kim and Gu 2006; Kim and Upneja 2014; Kwansa and Parsa 1991; Park and Hancer 2012; Parsa et al. 2021; Youn and Gu 2010), this study utilizes a more extended timeframe (20 years of data) from a comprehensive sample of publicly traded restaurant companies listed in the U.S. stock markets to identify the most accurate bankruptcy model for the restaurant industry, and latent functions or factors that could contribute to business failures in the restaurant industry.

Kim and Gu (2006) pioneered logistic regression (LOGIT) in the restaurant bankruptcy prediction model. Their study applied the logistic regression model to 32 companies in the hospitality sector (16 in bankruptcy and 16 not bankrupt) to predict the probability of a firm filing for Chapter 11 bankruptcy two years before the filing and found that logistic regression correctly predicted outcomes with 94%, slightly superior to MDA’s accuracy of 92%. Their data sample contains both restaurant firms and casinos. Low EBIT and high leverage are the key contributing factors. Youn and Gu (2010) recommended the logistic model as the preferred method compared to artificial neural network (ANN) for predicting restaurant firm failures in the U.S. by analyzing 37 firms that filed for bankruptcy. Park and Hancer (2012) utilized a sample of 80 companies (40 bankrupts and 40 nonbankrupts), encompassing hotel companies, restaurants, and entertainment services, and compared the logit model and ANN. They found that both models performed exceptionally well, that financial leverage was a significant variable, and that neural networks predicted better within the sample.

While previous studies have applied different bankruptcy models to the restaurant industry worldwide to determine the best model for predicting business failure or bankruptcy varies across countries, those studies include firms classified as dining places, which could include casinos, as in the case of (Kim and Gu 2006), across different countries, and have more limited data windows (before 2008). Since generally accepted accounting principles (GAAPs) differ among different countries, and misclassification could muddy the accuracy of the outcomes, we utilize only publicly traded restaurant firms in the U.S. with 25 years’ worth of data in this study.

3. Data and Methodology

The data for this study comprised publicly traded Eating Places with the 5812 SIC Code and Full-Service Restaurants with the 722110 NAICS Code, all listed in the Securities and Exchange Commission (SEC, accessed via EDGAR). The data included all 455 publicly traded restaurant companies listed in the SEC. The subset of the data used in this study consisted of restaurant companies that filed for bankruptcy petition under Chapter 11 over 25 years (from 1995 to 2019). In total, 36 restaurant companies filed for Chapter 11 protection during this period. We extracted the financials (the balance sheet, income statement, and statement of cash flow) from their annual report (10-K) filed one year before bankruptcy. To compare two different datasets (bankrupted vs. not bankrupted) to understand factors of bankruptcy, unbiased data comparison, benchmarking, risk assessment and management, and strategy development, we randomly selected 36 nonbankrupted restaurant firms from the same SIC code for the same period that matched the asset size of the firms that filed for Chapter 11.

The lists of 36 bankrupted and 36 nonbankrupt restaurant firms are presented in Appendix A and Appendix B. It is worth noting that during the study period from 2001 to 2019, two recessions occurred: the first from 2001 Q1 to 2001 Q3 and the second from 2007 Q4 to 2009 Q2. These recessions triggered a business failure risk for restaurant firms, with a 47% turnout ratio, indicating that 47% of the bankrupted restaurant firms filed for bankruptcy during these two recession periods. We chose 2019 as the cutoff point for our data to avoid the noises introduced by the volatilities in the supply-chain-induced price changes.

Selection for Independent Variables

Previous studies for predicting restaurant bankruptcies mainly utilized accounting and financial ratios that fall into five categories: liquidity, profitability, leverage, efficiency, and solvency ratios (Gu 2002; Kim and Gu 2006; Kim and Upneja 2014; Parsa et al. 2021; Youn and Gu 2010). Our study provides a more in-depth analysis by focusing on the following three concepts:

(1): Efficiency ratios measure how well a restaurant manages its resources, such as inventory.
(2): Effectiveness ratios measure how healthy assets are utilized to generate sales and profits.
(3): Performance ratios measure how well the firms meet short- or long-term obligations through leverage and solvency ratios (Abidin et al 2021; Gu 2002; Kim and Gu 2006; Kim and Upneja 2014; Youn and Gu 2010).

We then apply MDA and logistic regression analyses to these variables and compare the model’s performances. Table 1 shows the complete list of variables.

The assessment of restaurants’ net liquid assets relative to their total capitalization involved utilizing several vital ratios:

Current Ratio, Quick Ratio, and EBITDA/Current Liabilities: These metrics were employed to gauge the net liquid assets of the restaurants concerning their total capitalization.
We used the Total Liabilities/Total Assets ratio to measure financial leverage, indicating the proportion of a company’s debt-financed assets. Including EBITDA (Earnings Before Interest, Taxes, Depreciation, and Amortization) in the evaluation emphasizes its significance as a widely recognized measure of a company’s financial health and cash generation capability.
EBITDA/Total Liabilities (E TL) and EBIT/Interest Expenses (E Interest): We utilized these ratios to assess solvency, focusing on the capacity to meet long-term financial obligations.
Net Income/Total Sales and Net Income/Total Assets: These metrics were applied to gauge cumulative profitability over time, offering insights into the efficiency of generating profits relative to sales and assets.
Cost of Goods Sold/Average Inventories (C Inventory) and Total Revenues (T.R.)/Average Total Assets (Avg TA): These ratios were employed to measure operating efficiency, specifically assessing inventory management and asset utilization in generating revenues.

By employing this more diverse set of ratios, the analysis provides a more comprehensive view of the restaurants’ financial health. This approach allows for a more nuanced understanding of the factors contributing to these establishments’ overall financial performance.

4. Empirical Results

4.1. Multiple Discriminant Analysis

We start with the multiple discriminant analysis. Table 2 shows the summary statistics of the data set used for this study. Discriminant analysis reveals the mean and standard deviation of 10 accounting ratios for bankrupt and nonbankrupt firms.

As indicated by the mean values of the two groups (bankrupted vs. nonbankrupted) in the table, nonbankrupted firms exhibit higher ratios compared to bankrupted firms, particularly in solvency measures (e.g., EBIT/Interest Expenses, with values of 12.2661 and −42.4419, respectively). Notably, solvency has a substantial standard deviation across all groups, followed by efficiency metrics (e.g., inventory turnover). We can attribute this variance to factors such as the diverse asset sizes of these firms and their operational characteristics, including the number of units, years of operation, stock market trading, or participation in initial public offerings (IPOs).

Table 3 presents the results of Wilks’s lambda and univariate ANOVA used to evaluate the significance of differences between the means of accounting ratios for the two groups. According to the table, Net Income/Total Assets (F value: 12.031, p < 0.001) exhibits the most substantial significant difference between the groups, followed by Earnings/Total Liabilities (F value: 6.799, p = 0.011), Total Liabilities/Total Assets (F value: 6.549, p = 0.013), and Net Income/Total Sales (F value: 5.245, p = 0.025), respectively.

We undertook a discriminant analysis to assess the predictive capacity of ten accounting ratio predictors in forecasting the risk of bankruptcy or business failure. The global significance of the analysis was established, with a noteworthy overall Wilks’ lambda of 0.683 (Chi-square, χ²(10, N = 72) = 24.377, p = 0.007) signifies that, on the whole, the set of predictors effectively differentiated between the two groups, as detailed in Table 4.

In Table 5, the standardized canonical discriminant function coefficients elucidate the associations between the predictor variables (independent variables) and the canonical discriminant functions. The standardized discriminant function coefficients serve as a metric to evaluate the significance of each independent variable’s distinctive contribution to the discriminant function. These coefficients reveal that the current ratio makes a relatively high positive contribution, while the quick ratio predictor variable exhibits a negative relationship.

The estimated function is as follows:

Z = 5.620CR − 5.625QR − 0.660EBITD/CL − 0.233TD/TL + 0.816EBIT/TL + 0.021TIE − 1.84PM + 1.90ROA + 0.393ITO − 0.271TAT

As depicted in Table 6, the classification results indicate an approximate 80% group membership prediction rate. Within the success group comprising 36 firms, 27 (77.1%) were accurately predicted. A total of 29 out of 36 firms (80.6%) were correctly classified in the failure group. Out of the sample of 72 firms, the overall number of accurately classified firms was 56 (78.9%). While robust, our study’s robust prediction rate is slightly lower than the 94% correct classification rates reported by Kim and Gu (2006).

4.2. Logistic Regression

Considering the binary nature of the dependent variable (bankrupt v. nonbankrupt), a logistic regression model is particularly well suited. This modeling approach facilitates predicting the probability of an event occurring for an individual firm, particularly in predicting whether a firm’s risk is associated with a specific set of accounting ratios.

The comprehensive assessment of the model, as indicated in the “Omnibus Tests of Model Coefficients”, is gauged by the likelihood ratio (L.R.) test results. This test determines whether including the block of variables significantly enhances the model’s explanatory power. Table 7 reveals that the model is statistically significant, with χ²(10) = 31.393 and p < 0.001, signifying a substantial contribution from the set of variables in predicting the outcome.

This table includes the Cox and Snell R square and Nagelkerke R square, which are coefficients of determination (R²) providing insights into the extent of variation in y explained by the model. The calculated explained variation in the dependent variable (business failure) ranges from 35.7% to 47.6%, respectively. Specifically, the model elucidated 47.6% (Nagelkerke R square) of the variance in business failure and accurately classified 73.3% of cases. Notably, an increase in the current ratio was associated with an elevated likelihood of business success, while a decrease in the quick ratio was linked to business failure. Some practical suggestions for companies to pay attention to short-term liquidity management are as follows:

(1): The company should define a specific threshold value for these ratios. For example, a current ratio below 1.5 might trigger a review of financial management practices.
(2): Develop action plans for when ratios fall below acceptable levels. This could involve negotiating better credit terms with suppliers, optimizing inventory levels, or securing short-term financing.

Next, we conduct a robustness test of the models. The Hosmer and Lemeshow test assesses whether the model’s predictions align well with observed group memberships (see Table 8).

A chi-square test with χ²(8) = 10.491 compares the observed frequencies with those expected under the linear model. The result is nonsignificant, suggesting that the data fit the model well, indicating a satisfactory alignment between predicted and observed group memberships.

As evident in Table 9, logistic regression was utilized to estimate the probability of business risk (failure or success). A precise risk classification was achieved by employing a cutoff value of 0.50 probability. The results demonstrate accurate classifications for failure events at 71.4% and success events at 75.0%, resulting in an overall prediction rate of 73.2% accuracy. This classification table assesses the effectiveness of the predicted classification rate against the actual classification. The model exhibited 71.4% sensitivity in predicting restaurant firms that filed for bankruptcy and 75% specificity in classifying restaurants that did not undergo bankruptcy. Notably, the corrected prediction rate of the model on success (75%) slightly surpasses that of failure (71.4%). Our study’s prediction rate (73.3%) indicates lower correct classification rates than the rates Youn and Gu (2010) reported at 88.10%.

In Table 10, the section labeled “Variables in the Equation” summarizes the individual importance of explanatory variables while accounting for other variables.

The result of the logistic regression model is as follows:

ln[p/(1 − p)] = −0.350 + 8.794CR − 9.136QR − 0.248EBITDA/CL − 0.779TD/TL + 0.065TE/TL + 0.091TIE − 4.359PM + 3.520ROA + 0.024ITO − 0.279TAT

Examining the logistic coefficients for the two-variable model—specifically the current ratio (8.794) and quick ratio (−9.136)—reveals statistical and practical significance levels deemed acceptable across all accounting ratios as measures of overall model fit. The Wald test, employed to ascertain the statistical significance of each accounting ratio, indicates that both the current ratio (Wald: 4.697, sig = 0.030) and quick ratio (Wald: 4.75, sig = 0.029) contribute significantly to the model and prediction at the 0.05 level. However, despite being the most significant variable in the discriminant analysis (Wald: 1.520, sig = 0.218), Net Income/Total Assets did not add significant value to the model in this context. Hair et al. (2019) assert that the Exp(B), representing the odds ratio, signifies the predicted change in odds for a unit increase in the predictor. When Exp(B) is less than 1, increasing variable values correspond to decreasing odds of the event’s occurrence; a value of 1.0 equals no change in odds, and values above 1.0 indicate increases in the predicted odds (Hair et al. 2019).

This analysis uses the odds ratio (OR) to determine the probability of business failure compared to nonbusiness failure, calculated as Pf/(1 − Pnf). The current ratio (Exp(B)) suggests that assuming that all other accounting ratios remain constant, the odds of success/failure from business risk are 6593 times higher. Net Income/Total Assets follows suit, while the quick ratio (Exp(B) = 0.000) is less than 1, indicating a robust negative association that implies that every unit increase in the quick ratio corresponds to decreasing odds of failure occurrence.

Examining the logistic coefficients, the current ratio (8.794) shows a positive relationship, suggesting that as the current ratio increases, the predicted probability of a restaurant firm being categorized as a nonbankrupted, successful firm increases, thereby reducing the likelihood of business failure. Conversely, the quick ratio’s coefficient (−9.136) signifies a negative relationship, indicating that an increase in the quick ratio heightens the likelihood of a restaurant firm being categorized as bankrupt, leading to an increased probability of business failure.

Our study emphasizes the significance of two variables (current ratio, sig = 0.030, b: 0.8794, and quick ratio, sig = 0.029, b: −9.136), aligning with the findings of Youn and Gu. However, it is noteworthy that Young and Gu identified only one variable (return on assets, sig = 0.003, b: −30.52) as the most significant in determining the positive or negative relationship for predicting restaurant firm failure. This brings into question the efficacy of the study by Youn and Gu since cash flows and the ability to meet liquidity needs are more critical factors in determining the probability of bankruptcy in most industries. While the ability to generate net income (the numerator of ROA) is essential for the long term, most restaurants can sustain long periods of negative net income without filing for bankruptcy if the operating cash flow is positive.

Compare the predicted and actual groups for each observation to determine whether the observation was classified correctly. The results of predicted group membership (success or failure) for logistic regression and discriminant analysis models demonstrate the correct classification of original grouped cases by discriminant analysis at 78.9% and logistic regression at 73.2%, respectively. Discriminant analysis exhibits an 80.6% prediction rate for business failure and a 77.1% rate for nonfailure. Logistic regression shows 75% and 71.4%, respectively, suggesting that discriminant analysis generates a slightly higher correct prediction rate than logistic regression.

The stepwise logistic regression procedure results align closely with the two-group discriminant analysis. The final logistic regression model incorporates the current and quick ratios, with logistic regression coefficients of 8.794 and −9.136, respectively, and a constant of −0.350. Comparing these results to the two-group discriminant analysis reveals almost identical findings, with a current ratio of 5.620 and a quick ratio of −5.625.

Both discriminant analysis and logistic regression offer approaches for restaurant firms to comprehend the relative impact of each accounting ratio in differentiating between the two groups (i.e., business success or failure). Hair et al. (2019) recommends logistic regression because it robustly handles data conditions that can adversely affect discriminant analysis, such as unequal variance–covariance matrices and assumptions of multivariate normality. Logistic regression is considered equivalent to two-group discriminant analysis. It suits preferred estimation techniques in applications involving a single categorical dependent variable and several metric or nonmetric independent variables.

While both MDA and logistic regression offer similar efficacy in bankruptcy prediction, logistic regression is recommended due to its robustness in handling data conditions that can adversely affect discriminant analysis, such as unequal variance–covariance matrices and assumptions of multivariate normality. In other words, LOGIT does not require the predictor variables to be normally distributed or the covariance matrices to be equal, making it more flexible. Logistic regression is considered equivalent to two-group discriminant analysis and is suitable for preferred estimation techniques in applications involving a single categorical dependent variable and several metric or nonmetric independent variables

5. Conclusions

In conclusion, our study represents one of the most comprehensive analyses utilizing a large-scale, longitudinal dataset sourced from the SEC database. We collected data from publicly traded restaurant firms between 2000 and 2019 to test the predictability of various bankruptcy prediction models, increasing the sample size and accounting for a range of ratios over an extended study period. This enhanced model suggests that strategic management of liquidity ratios, particularly the current ratio, can mitigate restaurant firms’ business failure risk. In addition, we retrieved data for all 36 filed bankrupt firms and randomly selected 36 nonbankrupt restaurant firms from the same SIC code for the same period that matched the asset size of the firms that filed for Chapter 11. We used this data sampling method to understand bankruptcy factors, conduct unbiased data comparisons, benchmark, assess, and manage risk, and develop strategies. The industry-specific comparison, encompassing all publicly traded restaurants, adds robustness to our results.

While our models underscore the efficacy of financial ratios in determining bankruptcy, their applications extend beyond bankruptcy prediction. They offer valuable insights into restaurant management, small business owners, family businesses, and entrepreneurs. The current and quick ratios emerge as the most critical factors contributing to bankruptcy risk among the financial ratios considered. This implies that managing short-term liquidity should be the top priority for restaurant firms. A higher quick ratio value stands out as the ratio is highly correlated with a lower probability of bankruptcy, which means that the inventory value should be discounted at a higher rate for the restaurant industry than other industries in the retail sector.

Future research should explore the differential effects of external and internal factors on business failure, aligning with suggestions by Parsa et al. (2021). Investigating economic recession, location, restaurant density, household income, and internal factors such as cuisine type and health code violations can enhance prediction rates. As Altman recommended, extended examinations of firms over a longer period would enhance discriminant models’ reliability. Additionally, comparative analyses of bankruptcies during different periods, especially prepandemic, pandemic, and post-pandemic, are crucial for assessing external environmental impacts and validating bankruptcy prediction accuracy.

Author Contributions

Conceptualization, Y.H. and L.H.C.; methodology, Y.H.; validation, Y.H., L.H.C. and D.M.; formal analysis, Y.H. and D.M.; investigation, Y.H.; resources, Y.H.; data curation, Y.H.; writing—original draft preparation, Y.H., L.H.C. and D.M.; writing—review and editing, Y.H. and L.H.C.; supervision, Y.H. and L.H.C.; project administration, Y.H. and L.H.C. All authors have read and agreed to the published version of the manuscript.

Funding

The paper received no external funding. The APC was funded by department research funds.

Data Availability Statement

Data available upon request.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Bankrupted Firms	Year Filed	State	Coding	Total Assets ($)
Accredited Business Consolidators Corp (Italian Oven)	10/28/96	PA	1	17,892,818
Ameriking Inc.	12/11/02	IL	1	233,174
Bjs Restaurants Inc. (Chicago Pizza)	2001–4	CA	1	29,992,368
Boston Chicken Plan Trust	1998	AZ	1	1,543,616
Briazz Inc.	2004	WA	1	6963
Buffets Holdings, INC	2009	MN	1	579,767
Cooker Restaurant Corp	5/29/01	FL	1	97,618
Cucos Inc.	5/23/02	LA	1	3,147,813
Dennys Corp	7/24/97	SC	1	323,782
Donini Inc.	11/18/04	MA	1	1,458,558
El Chico	11/5/12	TX	1	47,662
Fine Host Corp	5/18/99	CT	1	243,123
Flagstar Corp	7/24/97	SC	1	1,513,828
Fog Cutter Capital Group Inc.	4/8/09	OR	1	27,573
FRD Acquisition Co	7/25/02	CA	1	123,920
Fresh Choice Inc.	12/21/05	CA	1	30,854
Furrs Restaurant Group Inc.	9/26/03	TX	1	76,649
interfoods of America Inc.	7/6/98	FL	1	117,028,224
Krystal Company	4/10/97	TN	1	146,917
Phoenix Restaurant Group Inc.	10/31/01	AZ	1	79,370
Planet Hollywood International Inc	5/9/09	FL	1	146,207
Prandium Inc.	10/18/03	CA	1	108,000
Pudgies Chicken Inc.	9/18/96	NY	1	1796135
Roadhouse Grill Inc.	1/18/02	FL	1	25,108
Ryans Restaurant Group Inc.	10/2/02	SC	1	706,828
Schlotzkys Inc.	4/21/06	TX	1	125,785,554
Shells Seafood Restaurants Inc.	9/3/08	Fl	1	11,478,818
Staceys Buffet Inc.	9/12/97	FL	1	5,922,937
Star Buffet Inc.	12/20/12	AZ	1	6998
Steakhouse Partners Inc.	5/20/08	CA	1	17,749
Stoico Restaurant Group Inc.	2/6/98	KS	1	5,119,448
TC Global Inc.	10/15/12	WA	1	8473
Vicorp Restaurants Inc.	4/8/08	CO	1	395,242
Wall Street Deli Inc.	10/3/01	AL	1	13,945,030
Watermarc Food Management Co.	1/15/99	TX	1	12,683,170
Worldwide Restaurant Concepts Inc.	8/27/97	CA	1	142,534

Appendix B

Nonbankrupted Firms	Coding	Total Assets ($)
ARK Restaurant	2	161,216
Buffets	2	552,986
Brinker International	2	2356
Applebee’s	2	935,456
Darden Int’l	2	10,656.1
MCD	2	33,803.7
Frisch’s Restaurants	2	129,011
Morton’ R	2	201,814
Max and Erma’s R	2	78,560,289
Noodles	2	172,032
Panchos	2	18,412
Sbarro	2	490,423
Sonic	2	531,134
Spaghetti	2	57,738
Uno Rest	2	168,476
Wendy’s	2	1,789,397
Organic to gp	2	12,940
Brazil Fast Food	2	110,885
Nathan’s Famous	2	80,091
Perkins and Marie Calenders	2	291,641
Rubio	2	74,701
NPC International	2	825,228
PF Chang	2	576,075
Ruby Tuesday	2	723,642
Texas Road	2	1,330,623
Star Buffet	2	6998
Papa Muphy	2	246,174
Luby’s	2	199,989
CKE	2	1,480,138
Jack In the Vox	2	823,397
Bravo Brion Rest	2	142,167
Garden Fresh Rest	2	153,006
Summit Family Re	2	70,884,000
Carrols Rest	2	581,514
Cheesecake Factory	2	1,333,060
Benihana/BJ	2	684,958

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Table 1. Ratios used for verifying the bankruptcy model.

Liquidity

Current Ratio

Quick Ratio

Earnings before interest and taxes and depreciation and amortization (EBITDA)/Current Liabilities

Financial Leverage

Debt Ratio: Total Liabilities/Total Assets

Solvency

EBITDA/Total Liabilities

EBIT/Interest Expenses

Profitability

Net Income/Total Sales

Net Income/Total Assets

Efficiency

Cost of Goods Sold/Average Inventories

Total Revenues/Averages Total Assets

Table 2. Mean and standard deviation of bankrupted vs. nonbankrupted firms.

Failure (Bankrupted Firms)	Mean	Std. Deviation
Current Ratio	0.6355	0.89981
Quick Ratio	0.5249	0.87868
EBITDA CL	0.5527	3.42020
TL LA	1.2540	1.01790
E TL	−0.0395	0.34380
E Interest	−42.4419	221.41035
Net Income T.S.	−0.1292	0.29953
Net Income TA	−0.2639	0.40793
C Inventory	27.2897	17.89250
TR Avg TA	1.9027	1.06504
Success (Nonbankrupted Firms)	Mean	Std. Deviation
Current Ratio	0.8093	0.67119
Quick Ratio	0.6301	0.66119
EBITDA CL	0.6113	0.83980
TL LA	0.7803	0.43887
E TL	0.1594	0.29790
E Interest	12.2661	32.26533
Net Income T.S.	−0.0014	0.14721
Net Income TA	−0.0061	0.17779
C Inventory	32.0520	25.92193
TR Avg TA	1.5870	0.71906

Table 3. Tests of equality of group means.

	Wilks’ Lambda	F	df1	df2	Sig.
Current Ratio	0.988	0.854	1	69	0.359
Quick Ratio	0.995	0.327	1	69	0.570
EBITDA CL	1.000	0.010	1	69	0.921
TL LA	0.913	6.549	1	69	0.013
E TL	0.910	6.799	1	69	0.011
E Interest	0.970	2.152	1	69	0.147
Net Income T.S.	0.929	5.245	1	69	0.025
Net Income TA	0.852	12.031	1	69	<0.001
C Inventory	0.988	0.807	1	69	0.372
T.R. Avg TA	0.970	2.154	1	69	0.147
Current Ratio	0.988	0.854	1	69	0.359

Table 4. Wilks’ lambda test of function(s).

Wilks’ Lambda Test of Function(s)	Wilks’ Lambda	Chi-Square	df	Sig.
1	0.683	24.377	10	0.007

Table 5. Standardized canonical discriminant function coefficients.

Function 1
Current Ratio (C.R.)	5.620
Quick Ratio (QR)	−5.625
EBITDA/CL	−0.660
TD/TA	−0.233
EBIT/TL	0.816
Time Interest Earned (TIE)	0.021
Profit Margin (PM)	−0.184
ROA	0.190
Inventory Turnover (ITO)	0.393
Total Asset Turnover (TAT)	−0.271

Table 6. Predicted group membership.

		Predicted Group Membership
		Success or F	1	2	Total
Original	Count	1	27	8	35
		2	7	29	36
	%	1	77.1	22.9	100.0
		2	19.4	80.6	100.0

A total of 78.9% of initially grouped cases were correctly classified.

Table 7. Omnibus tests of model coefficients.

Omnibus Tests of Model Coefficients
	Chi-Square	df	Sig.
Step 1	Step	31.393	10
	Block	31.393	10
	Model	31.393	10
Model Summary
Step	−2 Log likelihood	Cox and Snell R Square	Nagelkerke R Square
1	67.020 ^a	0.357	0.476

^a. Estimation terminated at iteration number 9 because parameter estimates changed by less than 0.001.

Table 8. Hosmer and Lemeshow test.

Hosmer and Lemeshow Test
Step	Chi-Square	df	Sig.
1	10.491	8	0.232

Table 9. Classification table.

	Observed	1	2	Percentage Correct
Step 1	Success	25	10	71.4
	F	9	27	75.0
	Overall Percentage			73.2

The cut-off value is 0.500.

Table 10. Variables in the equation.

Variables in the Equation
		B	S.E.	Wald	df	Sig.	Exp (B)
Step 1	CR	8.794	4.058	4.697	1	0.030	6593.140
	QR	−9.136	4.190	4.754	1	0.029	0.000
	EBITDA/CL	−0.248	0.240	1.066	1	0.302	0.780
	TD/TA	−0.779	0.667	1.366	1	0.243	0.459
	TE/TL	0.065	2.207	0.001	1	0.977	1.067
	TIE	0.091	0.060	2.304	1	0.129	1.096
	PM	−4.359	3.127	1.943	1	0.163	0.013
	ROA	3.520	2.855	1.520	1	0.218	33.786
	ITO	0.024	0.017	2.038	1	0.153	1.024
	TAT	−0.279	0.404	0.477	1	0.490	0.756
	Constant	−0.350	1.196	0.086	1	0.769	0.704

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Huo, Y.; Chan, L.H.; Miller, D. Bankruptcy Prediction for Restaurant Firms: A Comparative Analysis of Multiple Discriminant Analysis and Logistic Regression. J. Risk Financial Manag. 2024, 17, 399. https://doi.org/10.3390/jrfm17090399

AMA Style

Huo Y, Chan LH, Miller D. Bankruptcy Prediction for Restaurant Firms: A Comparative Analysis of Multiple Discriminant Analysis and Logistic Regression. Journal of Risk and Financial Management. 2024; 17(9):399. https://doi.org/10.3390/jrfm17090399

Chicago/Turabian Style

Huo, Yang, Leo H. Chan, and Doug Miller. 2024. "Bankruptcy Prediction for Restaurant Firms: A Comparative Analysis of Multiple Discriminant Analysis and Logistic Regression" Journal of Risk and Financial Management 17, no. 9: 399. https://doi.org/10.3390/jrfm17090399

APA Style

Huo, Y., Chan, L. H., & Miller, D. (2024). Bankruptcy Prediction for Restaurant Firms: A Comparative Analysis of Multiple Discriminant Analysis and Logistic Regression. Journal of Risk and Financial Management, 17(9), 399. https://doi.org/10.3390/jrfm17090399

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