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Statistical analysis of the effectiveness of company's accounts receivable
Based on of data of company's receivables by major debtors there can be evaluated the effectiveness of management using the methods of statistical analysis of variations. These, above all, are such indicators as the weighted arithmetic mean, mode, median, concentration ratio and the uneven distribution of attribute (accounts receivable). In the latter case it comes to the legitimacy of using the Gini coefficient, Herfindahl, variations, as well as graphic illustrations of uneven distribution of debtors using the Lorenz curve.
Obtaining analytical statistical tables, which allows to determine the characteristics of the of the variation series of accounts receivable of the enterprise involves a series computational actions.
1. Determining the optimal number of groups for the collection of debtors.
At this stage, application of Sturges formula is appropriate:
r = 1 + 3,32 lg n = 1 + 1,44 ln n, (2.7.1)
where n - number of population units (enterprises-debtors).
Since n = 45 (the number of debtors, according to Appendix 1)
r = 1 + 1.44 ln n = 1 + 1.44 ln (44) ≈ 6.45, number of groups can be taken as 6, i.e. r = 6.
Establishment of interval variational series of debtors
Intervals are set regarding to concentration of accounts receivable (see column A, table 2.7.1)
Table 2.7.1. The calculation of basic statistical characteristics of variational series of accounts receivable of the enterprise by major debtors
Accounts receivable, thousand rur
|
Number of debtors
|
Interval mean, xi
|
ximi
|
Cumulative frequencies Fi
|
Relative cumulative frequencies Pi, %
|
Distribution density, %,
|
Proportion of acc. rec. of groups of debtors in total
|
|
|
Yk = wi /
|
xk – 1
|
xk
|
mi
|
in % to total, wi
|
/ xk
|
|
Cumulative, qi
|
А
|
B
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
0
|
10
|
14
|
31,1
|
5
|
70
|
14
|
31,1
|
3,11
|
0,0010
|
0,0010
|
0,000001
|
350,00
|
10
|
100
|
6
|
13,3
|
55
|
330
|
20
|
44,4
|
0,15
|
0,0046
|
0,0056
|
0,000022
|
18 150,00
|
100
|
500
|
12
|
26,7
|
300
|
3600
|
32
|
71,1
|
0,07
|
0,0507
|
0,0563
|
0,002571
|
1 080 000,00
|
500
|
1 000
|
4
|
8,9
|
750
|
3000
|
36
|
80,0
|
0,02
|
0,0423
|
0,0986
|
0,001785
|
2 250 000,00
|
1 000
|
10 000
|
8
|
17,8
|
5500
|
44000
|
44
|
97,8
|
0,0020
|
0,6197
|
0,7183
|
0,384051
|
242 000 000,00
|
10 000
|
30 000
|
1
|
2,2
|
20000
|
20000
|
45
|
100,0
|
0,0001
|
0,2817
|
1,0000
|
0,079349
|
400 000 000,00
|
|
Total
|
45
|
100
|
|
71000
|
|
|
|
1
|
|
0,46778
|
645 348 511,00
|
The calculation of the average characteristics of interval variations of the series: a weighted average, mode and median
The weighted average will be:
(2.7.2)
Mode (Mo) for a series with unequal intervals is determined using a density distribution of (Yk). This is feature value that occurs most often in units of the aggregate. For a discrete series mode will be the option with the greatest frequency
Distribution density is the highest in group 1:
Yk = Y1 = 2,96.
(2.6.3)
Median (Me) is a feature value falling in the middle of a ranked set (for ranged series with an odd number of individual values of the median would be the value, which is located in the center of the series, in this case 44 / 2 = 22), is calculated using the cumulative frequency index:
(2.7.4)
The same value is obtained if we use the cumulative relative frequency.
(2.7.5)
Calculation of variation
Dispersion (D):
(2.7.6)
Standard deviation:
(2.7.7)
Coefficient of variation:
(2.7.8)
Calculation of the Gini concentration coefficient (G)
This ratio is used to measure the degree of uneven distribution of population units (accounts receivable of the company in 2009). This ratio it is appropriate to define by formula:
(2.7.9)
where Pi and Pi + 1 are consecutive values of the accumulated relative frequencies;
qi and qi + 1 are consecutive values of the elements of column 9 table 1;
qi (i =) are calculated according to the cumulative elements of column 8 table 1.
The results of support the calculations required to obtain the value of the Gini coefficient are given in Table 2.7.2.
(2.7.10)
Table 2.7.2. Intermediate estimates for the Gini coefficient of uneven distribution of accounts receivable of the company
Piqi+1
|
Pi+1qi+
|
29,5*0,0056=
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0,164411076
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43,2*0,0009=
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0,039575
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43,2*0,0563=
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2,429945947
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7,05*0,0056=
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0,392057
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70,5*0,0985=
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6,941808209
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79,5*0,0563=
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4,476216
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79,5*0,7183=
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57,13672669
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97,7*0,0985=
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9,62896
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97,7*1=
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97,72727273
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100*0,7183=
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71,82903
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Total:
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164,4001646
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Total:
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86,36584
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Establishing Herfindahl coefficient
This ratio indicates the total proportion of the dominant group among the debtors of the company (H) and is calculated as follows:
(2.7.11)
In accordance with data in table 2.7.1. H (%) = 46,78%
The calculation of the asymmetry coefficient of Pearson (Kas)
(2.7.12)
Using the Table. 2, there can be constructed Lorentz curve. On a horizontal axis there will be located cumulative relative frequency (Pi), and on a vertical there will be values of the parameters qi. Coordinates of the points the diagonal line correspond to equal values of the pair (Pi, qi). They are increasing multiple of 100 / 6 = 16.67.
Lorenz curve of uneven distribution of accounts receivable of analyzed company in 2009 is shown in Fig. 2.7.1.
Figure 2.7.1. Lorenz curve of accounts receivable distribution for 2009
Statistical indicators for assessing the distribution of enterprise's debtors by value of their debt may be used to assess the effectiveness of current assets management, and above all, their most significant part - accounts receivable. Table 2.7.3 represents the main statistical indicators of efficiency assessment for accounts receivable management.
Table 2.7.3. Main statistical indicators of efficiency assessment for accounts receivable management for 2009
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