Methods of setting up normative numbers of accountants[1]
Many pending questions worry accountant- managers, particularly setting up normative numbers for accountants as brain workers. Too many independent factors contribute to the scope & quantities of accounting staffs, in connection which rises necessary to proper choose appropriate indicators those stipulate highest correlation coefficient of paired dependence between exploring dimension & independent factors influenced that resulting dimension. Moreover usually practices using both indicators as total workers & sales revenue for determining normative numbers of accountants to classify economic entities in accordance their sizes. Herein we considered that possible to refer above cited showings if want to establish normative numbers of accountants. In this case correlation coefficients below computed by using empiric data collected with random survey have helped to overcome our doubts. Moreover that, contractual accountants, who engages in the line of providing outsourcing service & prepares financial statements under a contract for customers & wage settlement between them arranges on the basis of percentage related to saved salary of accounting staffs. Correlation coefficients (r) of selected paired dimensions have given as following: correlation coefficient between numbers of accountants & total workers is r = 0.975, & correlation coefficient between numbers of accountants & sales revenue is r = 0.996 respectively, & those illustrate powerfulness of relationship between surveyed indicators. Used following criteria table of confiding probability titled “Quantitative values of correlation coefficients applied to various rates of probability”[2] to estimate influences of paired dimensions by means of correlation coefficients. Table1
n | p=0.05 | p=0.02 | p=0.01 | n | p=0.05 | p=0.02 | p=0.01 |
1 2 3 4 5 | 0.996917 0.95000 0.8783 0.8114 0.7545 | 0.9995066 0.98000 0.93433 0.8822 0.8329 | 0.9998766 0.990000 0.95873 0.91720 0.8745 | 16 17 18 19 20 | 0.4683 0.4555 0.4438 0.4329 0.4227 | 0.5425 0.5285 0.5155 0.5034 0.4921 | 0.5897 0.5751 0.5614 0.5487 0.5368 |
6 7 8 9 10 | 0.7067 0.6664 0.6319 0.6021 0.5760 | 0.7887 0.7498 0.7155 0.6851 0.6581 | 0.8343 0.7977 0.7646 0.7348 0.7079 | 25 30 35 40 45 | 0.3809 0.3494 0.3246 0.3044 0.2875 | 0.4451 0.4093 0.3810 0.3578 0.3384 | 0.4869 0.4487 0.4182 0.3932 0.3721 |
11 12 13 14 15 | 0.5529 0.5324 0.5139 0.4973 0.4821 | 0.6339 0.6120 0.5923 0.5742 0.5577 | 0.6835 0.6614 0.6411 0.6226 0.6055 | 50 60 70 80 90 100 | 0.2732 0.2500 0.2319 0.2172 0.2050 0.1946 | 0.3218 0.2948 0.2737 0.2565 0.2422 0.2301 | 0.3541 0.3248 0.3017 0.2830 0.2673 0.2540 |
Selected indicators of total workers & sales revenue for a purpose of determining normative numbers of accountants provide favorable possibilities to compute normative numbers of accountants in alternatively, foresee their future trend & also smooth out workload for every staff properly. Let’s compute normative numbers of accountants for newly established company ABC by means of basic of collected empiric data for several companies, which deal with the similar activities. Table2
Number of accountants, y | Sales revenue, million MNT, x2 | ||||||
10 | 100 | 200 | 450 | 750 | 1000 | ||
Number of workers, x1 | 10 | 0.5 | |||||
50 | 1 | ||||||
100 | 2 | ||||||
150 | 4 | ||||||
200 | 6 | ||||||
250 | 9 | ||||||
Herein we have fond theoretic assumption in 3 alternative versions given below:
First. To calculate resulting equation y = f(x1) in the manner of dependence respected to total workers(x1).
Second. To yield resulting equation y = f (x2) in the manner of dependence respected to sales revenue(x2).
Third. To obtain resulting equation y =f (x1,x2) in the manner of dependence corresponded to both combined factors as total workers(x1) as well as sales revenue(x2). Below given statistical calculations needed in obtaining appropriate normal equations. Table2
y | y2 | x1 | yx1 | x2 | yx2 | x12 | x22 | x1x2 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
0.5 | 0.25 | 10 | 5 | 10 | 5 | 100 | 100 | 100 |
1 | 1 | 50 | 50 | 100 | 100 | 2500 | 10000 | 5000 |
2 | 4 | 100 | 200 | 200 | 400 | 10000 | 40000 | 20000 |
4 | 16 | 150 | 600 | 450 | 1800 | 22500 | 202500 | 67500 |
6 | 36 | 200 | 1200 | 750 | 4500 | 40000 | 562500 | 150000 |
9 | 81 | 250 | 2250 | 1000 | 9000 | 62500 | 1000000 | 250000 |
22.5 | 138.25 | 760 | 4305 | 2510 | 15805 | 137600 | 1815100 | 492600 |
Found below cited normal equations from relative sums denoted in columns of 1, 3, 4 & 7.
6ao+760a1 = 22.5
760ao+137600a1 = 4305.
a1 = 0.0352; ao = - 0.7087. Hence normative numbers of accountants via equation expressed as follows: ŷ = f(x1) = ao+ a1x1 = -0.7087 + 0.0352x1. Normative numbers of accountants could be found ŷ = f(x1oo) = ao+ a1x1oo = -0.7087 + 0.0352ּ100=2.81, if above mentioned company ABC has intended for planned 2012 to launch its activities with 100 workers. Herein possible to verify yielded results of theoretical numbers of accountants (ŷ)= f(x1) =22.5 by means of substitution primary empiric numbers of accountants into obtained theoretic equation ŷ = f(x1) = ao+ a1x1 = -0.7087 + 0.0352x1. Table3
Primary numbers of accountants, ( y ) | Theoretic numbers of accountants, (ŷ) | Variance on numbers , ∆= ŷ-y |
0.5 | - 0.7087 + 0.0352* 10 = - 0.35 | - 0.85 |
1 | - 0.7087 + 0.0352 *50 = 1.05 | 0.05 |
2 | - 0.7087 + 0.0352 *100 = 2.81 | 0.81 |
4 | - 0.7087 + 0.0352 * 150 = 4.57 | 0.57 |
6 | - 0.7087 + 0.0352*200 = 6.33 | 0.33 |
9 | - 0.7087 + 0.0352 * 250 = 8.09 | - 0.91 |
22.5 | 22.5 | 0 |
Obtains theoretical equation ŷ = f(x2) = ao+ a2x2 = 0.2548 + 0.008355x2 via similar way as used in solving ŷ = f(x1). Has fond below cited normal equations from relative sums denoted in columns of 1, 5, 6 & 8 of table 2.
6ao+ 2510a1 = 22.5
2510ao+1815100a1= 15805.
a1 = 0.008355; ao = 0.2548. Also normative numbers of accountants would be expressed ŷ = f(x4oo) = ao+ a2x4oo = 0.2548 + 0.008355 *400 = 3.6, if given company ABC has budgeted for 2012 to sales output amounted to 400,0 million MNT.
Besides has obtained final equation y =f (x1,x2) in the manner of solution for both independent factors as total workers(x1) as well as sales revenue(x2) respectively, which influenced on normative numbers of accountants obviously.
6ao+ 760a1+2510a2 = 22.5
760ao+ 137600a1+ 492600a2= 4305
2510ao+ 492600a1+ 1815100a2= 15805. Hence expected theoretical equation of normative numbers of accountants in dependence with combined both factors as of x1 & x2 found as follows: ŷ =f (x1,x2) = ao+ a1x1+a2x2 = 0.35 - 0.00306x1 + 0.009054x2. Obtained theoretical equation revised by substitution into which corresponding empiric data as given below. Table4
Primary numbers of accountants, ( y ) | Theoretic numbers of accountants, (ŷ) | Variance on numbers , ∆=ŷ-y |
0.5 | 0.41= 0.35 - 0.00306*10 + 0.009054 *10 | -0.09 |
1 | 1.10 = 0.35 - 0.00306 *50 + 0.009054 *100 | 0.10 |
2 | 1.85 = 0.35 - 0.00306 *100 + 0.009054 *200 | -0.15 |
4 | 3.97 = 0.35 - 0.00306 *150 + 0.009054 *450 | -0.03 |
6 | 6.53 = 0.35 - 0.00306 *200 + 0.009054 *750 | 0.53 |
9 | 8.64 = 0.35 - 0.00306 *250 + 0.009054 *1000 | -0.36 |
22.5 | 22.5 | 0 |
Now let’s compute expected normative of accounting staffs for planned 2012, if steering board of company aimed to manage its activities as with nearly 100 workers & cope with output by 400,0 million MNT. ŷ =f (x1,x2) = ao+ a1x1oo+a2x4oo = 0.35 - 0.00306x1 + 0.009054x2 = 0.35 - 0.00306 ּ100 + 0.009054 ּ 400 ≈ 3.7accountants.
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