Abstract

This study develops a mathematical framework to analyze the time-series of profitability ratios across different stages of life cycle. This study extends the analysis of ratios in the early stages of a startup outlined by Laitinen (2017) to contribute to the life cycle research. The growth of expenditure is assumed to consist of the difference of two steady growth processes: stand-alone growth and growth of competition impact. If the growth rate of competition impact exceeds the stand-alone growth rate, an S-shaped curve as a life cycle is resulted. Each periodic expenditure is assumed to generate a proportionally identical flow of revenue with a constant internal rate of return (IRR) and distributed geometric lag structure. The firm is expensing in each period a fixed part of periodic expenditure and beginning-of-the-period assets. It is shown that the time-series of profitability ratios are sensitive especially to the rate of expense emphasizing the role of expense method in financial reporting. If the rate of expense is not consistent with the revenue lag, profitability ratios show strong divergent variation (spread) across the early years (birth stage) and during the decline stage. Thus, in particular in these stages, profitability ratios are unable to reflect IRR properly.

Highlights

  • For several hundred years, scientists using statistical analysis have observed the regulation of system evolution as an initial slow change followed by a rapid change and ending in a slow change again (Kucharavy & De Guio, 2015)

  • The findings show that there is a spread in profitability ratios between life cycle stages, even if the behavior of the firm does not change during its life

  • CONCLUDING REMARKS The objective of this study was to develop a mathematical model of a firm with limited resources under competition in order to analyze the behavior of profitability ratios across the stages of life cycle

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Summary

Introduction

Scientists using statistical analysis have observed the regulation of system evolution as an initial slow change followed by a rapid change and ending in a slow change again (Kucharavy & De Guio, 2015). Systems in general tend to follow the law of natural growth over time going through periods of birth, growth, maturity, decline, and death (Modis, 1994). This set of periods is called the life cycle of a system described by different S-shaped curves. The best-known mathematical function that produces an S-shaped curve is called a logistic function (Kucharavy & De Guio, 2015). This kind of S-shaped curve has many applications. A specific S-shaped curve is applied at the level of the firm to analyze the behavior of profitability ratios across the life cycle stages

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