Financial Statistics

Answer

Financial Statistics

Executive Summary

This report has provided relationship overview between net profit after tax and total assets for the 50 sampled companies through random sampling technique from 1536 companies provided in the excel sheet. The main analysis techniques in the report are correlation and linear regression analysis. It was evaluated that net profit after tax and total assets for the 50 selected random sample indicated strong positive association (rho=0.790). Additionally, the linear regression analysis indicated that total assets positively influence on the net profit after tax.

Financial Statistics

In the contemporary market, net profit in a company is determined by several econometric factors such as asset level a company has, market capitalization, total revenue among other factors in the economy. In light of this, this report will devise a model that can be applied to predict net profit after tax with total assets as the main explanatory variable. Additionally, the report will explore the relationship between total assets and net profit after tax for the 50 sampled companies using random sampling.

Data Analysis

Exploratory Data Analysis

In this section, presents descriptive statistics for the variables in the analysis. Descriptive analysis infers much on the spread of the data. The main graphical features are histogram, pie charts, bar graphs for the ordinal variables.

Figure 1: Histogram for Market Capitalization

Table 1: Descriptive analysis for Market Capitalization

Illustration on figure 1 and table 1 above display histogram and descriptive analysis respectively for market capitalization. Based on the histogram, it is evident that the data is skewed to the left. This implies that data violate normality assumption. The variable market capitalization has mean, kurtosis and skewness of 288586452.9, 16.8388 and 4.05595 respectively. The variable has leptokurtic distribution since kurtosis value is greater than value 3. There is lack of symmetry in the data.

Figure 2: Histogram of total assets

Table 2: Descriptive analysis for total assets

Illustration on figure 2 and table 2 above displays histogram and descriptive analysis respectively for total assets. Based on the histogram, it is evident that the data is skewed to the left. This implies that data violate normality assumption. The variable total assets has mean, kurtosis and skewness of 1294236558, 49.1953 and 6.9899 respectively. The variable has leptokurtic distribution since kurtosis value is greater than value 3. There is lack of symmetry in the data.

Figure 3: Histogram for total Revenue

Table 3: Descriptive Analysis for total Revenue

Illustration on figure 3 and table 3 above displays a histogram and descriptive analysis respectively for total revenue. Based on the histogram, it is evident that the data is skewed to the left. Therefore, there is lack of symmetry in the data. This implies that data violate normality assumption. The variable total revenue has mean, kurtosis and skewness of 308442407.6, 20.1765 and 4.2467 respectively. The variable has leptokurtic distribution since kurtosis value is greater than value 3.

Figure 4:  Histogram for Net Profit after tax

Table 4: Descriptive analysis for net profit after tax

Illustration on figure 4 and table 4 above displays a histogram and descriptive analysis respectively for net profit after tax. Based on the histogram, there is evidence of unimodal shape with zero value as the center of the origin. However, this is numerically evaluated using skewness value presented in table 4. The variable total revenue has mean, kurtosis and skewness of 10951803.94, 20.5411 and 4.4667 respectively. The data is negatively skewed thus the line of symmetry is shifted to the left side. The variable has leptokurtic distribution since kurtosis value is greater than value 3.

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Figure 5: Pie Chart for Company Status

Table 5: Descriptive analysis for Company Status

Illustration on figure 5 and table 5 above displays a pie chart and a frequency tabulation for company status. Evidently, delisted, suspended and trading company proportions stood at 32.0%, 4.0% and 64% respectively.

Figure 6: Pie Chart for GCIS Sector

Table 6: Frequency tabulation for GCIS Sector

Illustration on figure 6 and table 6 above displays a pie chart and a frequency tabulation for GCIS sector respectively. It is established that consumer discretionary, consumer staples and energy stood at 10.0%, 4.0% and 8.0% respectively. Additionally, it is established that financials, healthcare, industries and information technology stood at 20.0%, 10.0%, 8.0% and 12.0% respectively. The GCIS sectors materials, real estate and utilities stood at 24.0%, 2.0% and 2.0% respectively.

Figure 7: Pie chart for GCIS Industry Group

Table 7: Descriptive analysis for GCIS Industry Group

Illustration on figure 7 and table 7 above displays pie chart and frequency tabulation respectively for GCIS industry group. It is established that banks, capital goods, consumer durables & Apparel, consumer services stood at 2.0%, 6.0%, 2.0% and 2.0% respectively. It is established that diversified financials, energy, food &staples stood at 18.0%, 8.0% and 4.0% respectively. Health care equipment& services and materials stood at 2.0% and 24.0% respectively. Pharmaceuticals, biotechnology & life and real estate, retailing, software & services and utilities technology hardware & equipment stood at 8.0%, 2.0, 4.0%, 12.0% and 2.0% respectively.

Confidence Interval for Total Revenue and Total Assets for the Sample

In this section 95% confidence, CI is -22032.6328 for the upper limit while the upper confidence level is 933407.2994 for the total revenue for the GCIS sector of materials. The CI level is presented as follows:

The above confidence level implies that the researcher is 95% sure that the mean value for the total revenue for GCIS sector of materials is found between -22032.6328 and 933407.2994 range. Similarly, 95% confidence level for the total assets for all types of companies that are trading is presented as follows:

The range implies that the researcher is 95% sure that the mean for the total assets for all types of companies trading to be in the range -781092600 as the lower range while 3369565715 is the upper level.

The 95% confidence level for whole population for GCIS sector for materials is presented as shown below (type=materials):

The 95% confidence level for whole population (total assets) for GCIS for all types of industries is presented as shown below:

Evidently, there are clear variations in relation to mean and confidence levels for the two aspects in considerations. All the calculations for confidence level calculations are presented in the appendix section.

Hypothesis Testing

In this section, there is need to attest whether average total revenue for financials (GCIS) is greater than average total revenue for health care (GCIS) and whether average market capitalization differs for financials and materials industries. The main analysis technique is independent t test analysis.

Table 8. Right tailed t test for average total revenues for financials (GCIS)

Illustration on table 8 above displays right tailed t test to evaluate whether indeed average total revenues for financials (GCIS) is more than average total revenue for health care (GCIS). Hypothesis is set as follows:

Against;

It is established that t-stat (1.402) that is statistically at 0.05 alpha levels (p-value=0.0973) under right tailed test. It is established that t (0.05, df=13) =1.771. The stated null hypothesis is not rejected at 95% confidence level. The mean difference is positive one implying that total revenue for financials GCIS is greater than health care GCIS revenue.

Table 9. Right tailed t test for average market capitalization for financials (GCIS)

Illustration on table 9 above displays two tailed t test to evaluate whether indeed average market capitalization for financials (GCIS) differs from average total capitalization for materials care (GCIS). Hypothesis is set as follows:

Against;

It is established that t-stat (1.245) that is statistically at 0.05 alpha levels (p-value=0.2446) under two tailed test. It is established that t(0.05, df=20)=2.086. The stated null hypothesis is not rejected at 95% confidence level. The stated null hypothesis is not rejected at 95% confidence level for two-tailed test. Therefore, the average levels for market capitalization do not differ significantly for financials and materials.

Correlation and Regression Analysis

Figure 8: Scatter plot between net profit after tax and total assets

Table 10: Correlation Matrix

Figures 8 and 10 displays scatter plot and correlation matrix respectively to check the relationship level between net profit after tax and total assets. The scatter plot indicates that there is a positive linear relationship between net profit after tax and total assets. Numerically, it is established that the two variables have strong positive correlation levels (rho=0.790). This indicates presence of association between the two variables.

Regression Analysis

In this section, a linear regression model is fitted to predict net profit after tax with total asset as the main independent variable.

Table 11: Summary Statistics

Illustration on table 11 displays model’s summary. It is established that total asset accounts for 62.4514% variation of the net profit after tax (R-Square=0.6245). Additionally, adjusted R-Square is 0.616691. This is the variation accounted for by the independent variable after adjustments made with number of cases in the data. Anova table below evaluates whether the model is adequate at 0.05 alpha levels. 

Table 12: Anova Analysis

The F-ratio statistics is applied to test the following hypothesis for model adequancy.

H₀: β₁=β₂=…=β_i=0 for i=1, 2, 3…

Against

H₁: β₁≠β₂≠…≠β_i≠0 for i=1, 2, 3…

It is established that F (1, 48) =79.83432, p-value<0.010. The stated null hypothesis is rejected in favor of the alternative one at 95% confidence levels. This implies that the model is adequate at 0.05 alpha levels. In this case, total assets significantly influences on net profit after tax. Subsequently, a linear regression model is fitted based on results presented in table 13 below.

Table 13: Estimated Model Coefficients

A linear regression model is fitted as shown below:

The constant (β0=2467675) is net profit level after tax when explanatory variable (total asset) is set equal to zero value. The constant is statistically insignificant at 0.05 alpha levels (p-value=0.6569). It is established that the variable “total assets” has a positive coefficient of 0.006555 that is statistically significant at 0.05 alpha levels (p-value<0.010). One unit increase of the variable “total assets” increases net profit after tax with a magnitude of 0.006555 units. 

Conclusion

The report has evaluated the relationship between net profit after tax and total assets level for the 50 selected companies. The sample was randomly selected from a population of 1536 companies. The main analysis technique in the analysis was correlation and regression analysis. Correlation analysis established presence of strong positive relationship between net profit after tax and total assets level for the 50-selected sample.

Appendices

CI is calculated as follows:

 For total revenue for GCIS group sector of materials we have

For total assets for all types of companies, trading is calculated as follows:

For total revenue for all types of companies, trading is calculated as follows (whole population=materials):

For total assets for all types of companies, trading is calculated as follows (whole population):