Month: May 2023

Cracker Barrel (NASDAQ: CBRL), the restaurant and gift shop chain, is one of many successful businesses whose sales in constant dollars have stagnated after a period of rapid, even exponential growth. Historically, Cracker Barrel relied almost exclusively on roadside billboards and word of mouth for its dramatic growth from a small business in Lebanon, TN in 1969 to sales of about $2.4 billion in 2004. Adjusted by the US Consumer Price Index (CPI), Cracker Barrel’s 2022 sales were only $2.1 billion in 2004 dollars.

This decline in real sales has occurred despite or even because of a sustained attempt to diversify away from the historically successful billboard advertising into other media.

Is it possible to use modern Artificial Intelligence (AI) technologies such as ChatGPT or other less well known methods to boost Cracker Barrel or other businesses now stagnant sales?

This article examines Cracker Barrel’s publicly reported expenditures on billboards and other media using Artificial Intelligence based Math Recognition to evaluate the effectiveness of Cracker Barrel’s strategies since 2004, generally supporting the company’s focus on other media, now about two thirds of ad expenditures, although also indicating the effectiveness of current advertising methods whether billboards or “other media” is small compared to the spectacular results in the 1980’s and 1990s.

Indeed the public financial data suggests Cracker Barrel may be fighting a negative effect from growing US Gross Domestic Product (GDP), needing to advertise more and more simply to sustain, never mind boost, company revenues.

Cracker Barrel’s publicly available information on the company’s marketing and advertising expenditures is very limited, falling into two aggregate categories: billboards and “other media” which includes radio, TV, Internet, and other non-billboard methods. The data is annual for the entire United States. There is no geographical breakdown, association with specific marketing or advertising campaigns in time, location, or other important factors.

It is almost certain our Math Recognition would construct more complex models from such details and likely make more reliable predictions from more detailed data which Cracker Barrel undoubtedly has in the internal accounting systems than the relatively simple model constructed from the public data.

What is Math Recognition?

Math recognition is a key part of scientific and engineering practice. It is identifying and recognizing the mathematical formulas and objects describing the data. The Bell Curve often encountered in grading in high school or college is a well known and relatively easy to identify mathematical formula. In addition to grades it describes the frequency of heights in adults of the same sex and many other common measured quantities.

However, scientists, engineers, and financial analysts often struggle to find a viable mathematical formula or formulas for real world data. Without such a formula it is impossible to make predictions or optimize the output of systems.

Our Math Recognizer has a large and growing database of known mathematics including obscure and difficult to identify mathematical objects: special functions, differential equations, etc.. The Math Recognizer uses AI methods to recognize these mathematical formulas in data.

What is the mathematical relationship if any between a company’s advertising expenditures on competing methods and actual sales?

Half the money I spend on advertising is wasted; the trouble is, I don’t know which half.

John Wanamaker (1838-1922)

This is an OLD problem in business.

The Math Recognizer is able to identify a relatively simple mathematical model for the Cracker Barrel data combined with the US Gross Domestic Product (GDP) from the St Louis Federal reserve. The GDP is used as a proxy for the overall state of the economy, something the company cannot control. For example, in the revenues reported by Cracker Barrel we can easily see a sharp drop attributable to the 2020 COVID pandemic lockdowns, something clearly beyond the control of the company.

The model roughly “explains” about 86 percent of the variation in the data. This is a roughly correct interpretation of the R**2 or coefficient of determination Goodness of Fit (GoF) metric used in the analysis.

Once we have identified a model with good agreement with the data, we can optimize the output, meaning maximize the sales in this case, given a projected budget. This is actually somewhat disappointing in that the program recommends to spend the entire budget on the “other media,” non-billboard, category with a slight dip in sales due to the negative effect of GDP according to the model.

Let’s consider a larger future budget of $150 million, an abrupt increase of about $60 million over 2022. In this case we see the expected sales in current dollars to jump from about $3.2 billion in 2022 to almost $4 billion, an increase of about $800 million per year.

For this increase to pay for itself, the additional $800 million in sales must cost no more than $740 million dollars — a profit margin of about 7.5% (seven point five percent). That is a good profit margin for a restaurant. Restaurants often average only 3-5 percent profit margins.

Conclusion

A simple model based on broad financial numbers like these should not be taken very seriously although it may give some insights into a company. Indeed this simple analysis appears to support Cracker Barrel’s existing policies of diversifying advertising out of billboards, despite the disappointing results with inflation adjusted sales stagnant.

An in depth analysis of finely grained internal accounting data may be able to yield more detailed, reliable, and actionable results including a predictive model.

(C) 2023 by John F. McGowan, Ph.D.

About Me

John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).