An Estimation of the Capital Growth Rate in Business Activities

Author(s)
Bartosz Kurek

ABSTRACT

The aim of the paper is to empirically assess whether capital growth rates (defined as in the paper) realized by companies constituting Standard & Poor’s indices: S&P 600, S&P 400 and S&P 500 were higher in years prior to crisis, i.e. in years: 2007, 2006, 2005 than the average growth rates in preceding 5-year periods, i.e. in periods: 2002-2006, 2001-2005 and 2000-2004. A statistical test concerning the differences between means was used as a research method. In order to achieve that 9 hypotheses were tested in total. The further purpose of this paper is to estimate capital growth rates for every index in each of the years from 2000 up to 2007, as well as in 5- and 8-year periods. In total 40 confidence intervals for capital growth rates were constructed in order to achieve that goal. M. Dobija’s theory of capital was used as a background for a research. According to that theory capital is an abstract ability to perform labor. Homogeneous capital is embodied in heterogeneous assets. Capital is subdued to a number of laws: 1) the conservation principle and 2) the dispersion principle. These laws form the fundamentals of the theory of capital. The concentration of capital in any particular time moment is described in the form of the equation, where initial capital is influenced by the three factors: a natural potential of growth, a spontaneous diffusion and an inflow of capital by human labor and management. The natural potential of growth may be estimated by a properly defined ROA index. Realized ROA by a single company in a particular time period is a random number. However, in a large sample of companies, the average ROA index over a long time period concentrates around the natural potential for growth. The research shows that in most cases the capital growth rates were statistically higher in years prior to crisis than the average growth rates in preceding 5-year periods. Similarly—in most cases—the average rate of return on assets in each of the indices was increasing from year to year in nominal terms. That increased return on assets might strengthen the believes of investors that higher and higher profits are achievable on a regular basis. However, it seems that investors did not acknowledge that returns will float towards the average ultimately as the theory of capital describes.

The aim of the paper is to empirically assess whether capital growth rates (defined as in the paper) realized by companies constituting Standard & Poor’s indices: S&P 600, S&P 400 and S&P 500 were higher in years prior to crisis, i.e. in years: 2007, 2006, 2005 than the average growth rates in preceding 5-year periods, i.e. in periods: 2002-2006, 2001-2005 and 2000-2004. A statistical test concerning the differences between means was used as a research method. In order to achieve that 9 hypotheses were tested in total. The further purpose of this paper is to estimate capital growth rates for every index in each of the years from 2000 up to 2007, as well as in 5- and 8-year periods. In total 40 confidence intervals for capital growth rates were constructed in order to achieve that goal. M. Dobija’s theory of capital was used as a background for a research. According to that theory capital is an abstract ability to perform labor. Homogeneous capital is embodied in heterogeneous assets. Capital is subdued to a number of laws: 1) the conservation principle and 2) the dispersion principle. These laws form the fundamentals of the theory of capital. The concentration of capital in any particular time moment is described in the form of the equation, where initial capital is influenced by the three factors: a natural potential of growth, a spontaneous diffusion and an inflow of capital by human labor and management. The natural potential of growth may be estimated by a properly defined ROA index. Realized ROA by a single company in a particular time period is a random number. However, in a large sample of companies, the average ROA index over a long time period concentrates around the natural potential for growth. The research shows that in most cases the capital growth rates were statistically higher in years prior to crisis than the average growth rates in preceding 5-year periods. Similarly—in most cases—the average rate of return on assets in each of the indices was increasing from year to year in nominal terms. That increased return on assets might strengthen the believes of investors that higher and higher profits are achievable on a regular basis. However, it seems that investors did not acknowledge that returns will float towards the average ultimately as the theory of capital describes.

Cite this paper

B. Kurek, "An Estimation of the Capital Growth Rate in Business Activities,"*Modern Economy*, Vol. 3 No. 4, 2012, pp. 364-372. doi: 10.4236/me.2012.34047.

B. Kurek, "An Estimation of the Capital Growth Rate in Business Activities,"

References

[1] P. Viernimmen, P. Quiry, M. Dallocchio, Y. Le Fur and A. Salvi, “Corporate Finance: Theory and Practice,” John Wiley & Sons Ltd., Chichester, 2009.

[2] M. Dobija, “Abstract Nature of Money and the Modern Equation of Exchange,” Modern Economy, Vol. 2, No. 2, 2011, pp. 142-152. doi:10.4236/me.2011.22019

[3] M. Dobija, “Labour Productivity vs Minimum Wage Level,” Modern Economy, Vol. 2, No. 5, 2011, pp. 780-787. doi:10.4236/me.2011.25086

[4] “S&P Indices: The S&P MidCap 600,” Access on 2 January 2012. http://www.standardandpoors.com/indices/sp-smallcap-600/en/eu/?indexId=spusa-600-usduf--p-us-s--

[5] “S&P Indices: The S&P MidCap 400,” Access on 2 January 2012. http://www.standardandpoors.com/indices/sp-midcap-400/en/eu/?indexId=spusa-400-usduf--p-us-m--

[6] “S&P Indices: The S&P MidCap 500,” Access on 2 January 2012. http://www.standardandpoors.com/indices/sp-500/en/eu/?indexId=spusa-500-usduf--p-us-l--

[7] I. Fisher, “The Nature of Capital and Income,” Augustus M. Kelly Publisher, New York, 1965, pp. 53-57.

[8] E. von B?hm-Bawerk, “Capital and Interest, Vol. 2: Positive Theory of Capital,” Libertarian Press, South Holland, 1959, pp. 16-66.

[9] E. Majewski, “Capital: The Set of Core Phenomena and Concepts in Economy,” 4th Edition, E. Wende i ska, Warszawa, 1914.

[10] S. T. Skrzypek, “The Concept of Capital in Literature,” Nak?. Towarzystwa Naukowego, Pomerania, 1939.

[11] C. Bliss, “Capital Theory and the Distribution of Income,” North-Holland Publishing Company, Oxford 1975.

[12] Y. Ijiri, “Segment Statements and Informativeness Measures: Managing Capital vs Managing Resources,” Accounting Horizons, Vol. 9, No. 3, 1995, pp. 55-67.

[13] M. Dobija, “Abstract Nature of Capital and Money” In: L. M. Cornwall, Ed., New Developments in Banking and Finance, Nova Science Publishers, Inc., New York, 2007, pp. 89-114.

[14] F. L. Lambert, “Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms—Examples of Entropy Increase? Nonsense!” The Journal of Chemical Education, Vol. 76, No. 10, 1999, pp. 1385-1387. doi:10.1021/ed076p1385

[15] M. Dobija, “Fair Value as a Criterion of Truth in Economic Theory” In: W. Adamczyk, Ed., D??enie do Prawdy w Naukach Ekonomicznych, Akademia Ekonomiczna w Krakowie, Kraków, 2006, pp. 125-150.

[16] B. Kurek, “An Adjusted ROA as a Proxy for Risk Premium Estimation—The Case of Standard and Poor’s 1500 Composite Index,” Cracow University of Economics, Krakow, 2010, pp. 87-103.

[17] B. Kurek, “The Risk Premium Estimation on the Basis of Adjusted ROA,” In: I. Górowski, Ed., General Accounting Theory: Evolution and Design for Efficiency, Academic and Professional Press, Warsaw, 2008, pp. 375-392.

[18] R. A. DeFusco, D. W. McLeavey, J. E. Pinto and D. E. Runkle, “Hypothesis Testing,” In: Ethical and Professional Standards and Quantitative Methods (CFA Program Curriculum), Pearson Publishing, Boston, 2007.

[19] Z. Hellwig, “Elements of Probability Calculus and Mathematical Statistics,” 8th Edition, PWN, Warszawa, 1978, p. 214.

[20] B. Kurek, “Hypothesis of Deterministic Risk Premium,” Ph.D. Thesis, Cracow University of Economics, Kraków, 2011.

[1] P. Viernimmen, P. Quiry, M. Dallocchio, Y. Le Fur and A. Salvi, “Corporate Finance: Theory and Practice,” John Wiley & Sons Ltd., Chichester, 2009.

[2] M. Dobija, “Abstract Nature of Money and the Modern Equation of Exchange,” Modern Economy, Vol. 2, No. 2, 2011, pp. 142-152. doi:10.4236/me.2011.22019

[3] M. Dobija, “Labour Productivity vs Minimum Wage Level,” Modern Economy, Vol. 2, No. 5, 2011, pp. 780-787. doi:10.4236/me.2011.25086

[4] “S&P Indices: The S&P MidCap 600,” Access on 2 January 2012. http://www.standardandpoors.com/indices/sp-smallcap-600/en/eu/?indexId=spusa-600-usduf--p-us-s--

[5] “S&P Indices: The S&P MidCap 400,” Access on 2 January 2012. http://www.standardandpoors.com/indices/sp-midcap-400/en/eu/?indexId=spusa-400-usduf--p-us-m--

[6] “S&P Indices: The S&P MidCap 500,” Access on 2 January 2012. http://www.standardandpoors.com/indices/sp-500/en/eu/?indexId=spusa-500-usduf--p-us-l--

[7] I. Fisher, “The Nature of Capital and Income,” Augustus M. Kelly Publisher, New York, 1965, pp. 53-57.

[8] E. von B?hm-Bawerk, “Capital and Interest, Vol. 2: Positive Theory of Capital,” Libertarian Press, South Holland, 1959, pp. 16-66.

[9] E. Majewski, “Capital: The Set of Core Phenomena and Concepts in Economy,” 4th Edition, E. Wende i ska, Warszawa, 1914.

[10] S. T. Skrzypek, “The Concept of Capital in Literature,” Nak?. Towarzystwa Naukowego, Pomerania, 1939.

[11] C. Bliss, “Capital Theory and the Distribution of Income,” North-Holland Publishing Company, Oxford 1975.

[12] Y. Ijiri, “Segment Statements and Informativeness Measures: Managing Capital vs Managing Resources,” Accounting Horizons, Vol. 9, No. 3, 1995, pp. 55-67.

[13] M. Dobija, “Abstract Nature of Capital and Money” In: L. M. Cornwall, Ed., New Developments in Banking and Finance, Nova Science Publishers, Inc., New York, 2007, pp. 89-114.

[14] F. L. Lambert, “Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms—Examples of Entropy Increase? Nonsense!” The Journal of Chemical Education, Vol. 76, No. 10, 1999, pp. 1385-1387. doi:10.1021/ed076p1385

[15] M. Dobija, “Fair Value as a Criterion of Truth in Economic Theory” In: W. Adamczyk, Ed., D??enie do Prawdy w Naukach Ekonomicznych, Akademia Ekonomiczna w Krakowie, Kraków, 2006, pp. 125-150.

[16] B. Kurek, “An Adjusted ROA as a Proxy for Risk Premium Estimation—The Case of Standard and Poor’s 1500 Composite Index,” Cracow University of Economics, Krakow, 2010, pp. 87-103.

[17] B. Kurek, “The Risk Premium Estimation on the Basis of Adjusted ROA,” In: I. Górowski, Ed., General Accounting Theory: Evolution and Design for Efficiency, Academic and Professional Press, Warsaw, 2008, pp. 375-392.

[18] R. A. DeFusco, D. W. McLeavey, J. E. Pinto and D. E. Runkle, “Hypothesis Testing,” In: Ethical and Professional Standards and Quantitative Methods (CFA Program Curriculum), Pearson Publishing, Boston, 2007.

[19] Z. Hellwig, “Elements of Probability Calculus and Mathematical Statistics,” 8th Edition, PWN, Warszawa, 1978, p. 214.

[20] B. Kurek, “Hypothesis of Deterministic Risk Premium,” Ph.D. Thesis, Cracow University of Economics, Kraków, 2011.