The change of the correlation coefficient between the number of employees and asset size in different indicators over time(taking the industry of Energy and IT as examples).

The change of the correlation coefficient between the number of employees and asset size in different indicators over time(taking the industry of Energy and IT as examples).</p

GR PRFT_ SALES(The deviation <i>ζ</i> obtained when <i>X</i> takes SALES and <i>Y</i> takes GR PRFT, in Eq 4) vs. Profit ratio(GR PRFT / SALES).

GR PRFT_ SALES(The deviation ζ obtained when X takes SALES and Y takes GR PRFT, in Eq 4) vs. Profit ratio(GR PRFT / SALES).</p

Variables used.

Many studies have shown that scaling laws widely exist in various complex systems, such as living organisms, cities, and online communities. In this research, we found that scaling laws also hold for companies. The macroscopic variables of companies, such as incomes, expenses, or total liability, all have power-law relationships with respect to the sizes of companies, which can be measured by sales, total assets, or the total number of employees. What is more, we also found the power law exponents always deviate from 1. That means large companies naturally have certain advantages, but the widely used financial indicators based on total volume or ratio may not reflect the company’s status well because they are also size-dependent. To tackle this problem, this paper proposes a new set of evaluation indices based on the deviations of the macroscopic variables from the scaling law to eliminate the size-dependent effect. We found that the indicators based on deviations can give more reasonable evaluations for companies and can outperform other conventional indicators to predict the financial distress of companies.</div

Most related variables selected by COX+MCP method.

Most related variables selected by COX+MCP method.</p

The scaling law of sales and cash for publicly traded companies in the US in 2018.

The exponent is 0.78 which means the nonlinear effect on the ratio of cash/sales exists.</p

Ranking comparison radar chart of the Chinese market (2020).

Ranking comparison radar chart of the Chinese market (2020).</p

Scaling law of Chinese market between net income and total sales in 2020.

Scaling law of Chinese market between net income and total sales in 2020.</p

Different scaling law between cash with respect to sales for different industries in 2018 (sorted by <i>α</i>).

Different scaling law between cash with respect to sales for different industries in 2018 (sorted by α).</p

SG&A_SALES deviation(The deviation <i>ζ</i> obtained when <i>X</i> takes SALES and <i>Y</i> takes SG&A, in Eq 4) vs. SG&A/SALES.

SG&A_SALES deviation(The deviation ζ obtained when X takes SALES and Y takes SG&A, in Eq 4) vs. SG&A/SALES.</p

The average deviation of each industry in 1990 (the beginning year of the dataset) uses the employee scale.

The average deviation of each industry in 1990 (the beginning year of the dataset) uses the employee scale.</p