Factor Analysis Comparison of Factor Differences Between Old and New Calculation Methods

In this paper, following the previous: factor analysis, cost difference analysis of the status quo and existing problems; The allocation problem of the total difference caused by the factor interaction of factor analysis, and the application of a new factor analysis method: exponential logarithmic proportion method, make the factor analysis and difference analysis have a correct solution. This paper is mainly based on the above factor analysis of the "exponential logarithmic ratio" method, and the current American management accounting (Srikant m. atar et al.), cost and management accounting (Charles t. orngren et al.), and management accounting (Ray h. arrison et al.). China's current "applied statistics" and "financial analysis" (national excellent course); "Financial cost management" certified public accountant examination book "cost management accounting"; Countries "twelfth five-year" plan of undergraduate course of common higher education teaching materials "management accounting" as an example, through comparing traditional balance of substitution factor analysis method and index of logarithmic ratio method, two kinds of calculation method for the calculation results of difference comparison and draw the conclusion: the new method of factor analysis can correctly allocate factor interactions that main factors differences between factor can be decomposed into the sum of factor analysis the index of logarithmic ratio method can solve the problem of interaction between factors cannot be separated; It has solved the unsolvable problems that have troubled the factor analysis and difference analysis in economic management for many years, which not only has the function of theoretical perfection, but also has the guiding significance in practical activities.

The knowledge points of factor analysis involve many professional courses and are widely used in practice. This paper tries to compare the results of two kinds of calculation methods to find out the scientificity and correctness of the two different methods. Considering the relevance of factor analysis cases, this paper tries to cite influential and authoritative teaching materials at home and abroad as examples, and use the old and new methods of factor analysis to solve problems, so as to establish the scientificity and correctness of the new method. And it can correct the traditional factor analysis method.
In the current application of factor analysis, a lot of conditions and assumptions have been set, among which, the "order" of factors cannot be changed, and the "quantity before quality" hypothesis is adopted in the implementation of analysis.
Following on from the previous article «New Solution of Factor Analysis Difference in Factor Product Combination» On the basis of this, the author USES the exponential logarithmic proportion method to calculate and analyze the current relevant books, the cases of factor analysis and difference analysis, and compares the calculated results with the traditional solution results, so as to prove the correctness of the new factor analysis method. Considering the systematicness, completeness and consistency of the article combination, the structure and preambles of this paper should be considered as a whole to meet the normative requirements. Example 1. Financial Accounting by Roman l. eil, Katherine Schipper and Jennifer Francis. Translated by zhu Dan and qu tenglong. 1st edition p 175-176, China machinery industry press, September 2015 [1]. R0E=ROA* financial leverage To analyze the change difference of the return on equity of the main factor from 2012 to 2011, the basic theoretical formula of the analysis is: return on equity = net interest rate on sales * return on total assets. The two answers are completely different, because the interaction between the two factors is occupied by the replaced factor. Therefore, factors have different influences on major factors. The original book did not consider the factor structure of the factors and did not make detailed analysis of the factors. Instead, it directly calculated the difference between the return on equity of the main factors of the two years as 21.7-20.7=1, and did not specifically analyze the difference of the influence of the factors. Since it is the formula structure of multiplication, the factor analysis of factors cannot conclude that the sum of the influence difference between the two factors is 0.7+ (-0.13) ≠1.064. Only according to the factor analysis method, it can be concluded that the total difference is equal to the sum of the differences of the factors, 2.065+ (-1.001) =1.064. It is not clear what method the authors would use if the proposition were to refine the analysis of factors affecting the total.
The results calculated by the traditional method (taking the return on total assets as the first step) are compared with those calculated by the exponential logarithmic ratio In the traditional method, the impact of total return on assets on the return on equity is overcalculated by 0.047%, and the impact of financial leverage on the return on equity is overcalculated by -0.047%.
The influence amount of factors calculated by the exponential logarithmic ratio method is the same regardless of the order of factors, because this method has fairly distributed the interaction difference of the two factors' influence on the main factors.
Example 2. Basic analysis formula of turnover rate of accounts receivable: turnover rate of accounts receivable = sales revenue/average accounts receivable (same as above P 179).
When calculating and analyzing accounts receivable turnover rate = sales revenue * average accounts receivable^(-1), or accounts receivable turnover rate = average accounts receivable^(-1)* sales revenue, the influence amount of factors on the main factors is completely different. For the two order of factors, the results of the factors' influence on the population calculated by traditional factor analysis are completely different. Once again, because of the interaction of factors, it is assumed by one of the factors. The exponential logarithmic ratio method gives the same result no matter how the order of the factors is changed, because this method fairly allocates the interaction between the two factors.
The original book answer is: 2012 accounts receivable turnover ratio decreased 6.6 compared with 2011. The overall difference is made directly: 25.6-32.2=-6.6. Without the use of factor analysis method, the specific influence amount of the sub-factors "sales revenue" and "average accounts receivable" that affect the main factor "accounts receivable turnover rate" is further decomposed, avoiding the problem of apportionment of the interaction of factors in the product structure. It is not possible to analyze the specific difference of sales revenue and average accounts receivable in affecting the turnover rate of accounts receivable (-6.6), so as to figure out the influence degree of specific factors and the power and responsibility relationship that the corresponding responsible subject should bear.

Interaction is Not the Quantity of Breeding Factors
The current factor analysis results in many factors other than the main factors, such as "structure", "rank" and "efficiency". Some are complex variables, some are variables other than factors, it is really confusing, some seem to cover up the interaction between factors, is derived from the factors of variables, such as: structure, actually derived from the amount and amount; Grade is the factor derived from the price of mixed portfolio; Efficiency is derived from unit hours and product costs.
In the author's opinion, these derived factors actually play a role in explaining the unexplainable interaction, thus leading to the regret that the whitewashing method has defects. Example 3. In kanter, M, Dartmouth's (Srikant m. atar) Madhav, V, rajan (Madhav V. R ajan) [M]. "management accounting" (Wang Liyan, ChenJia seats, renmin university of China press, on April 1, 2015,) of chapter 13 "flexible budget, differences and management control" [2] p 461-463 price difference and efficiency difference (the original book answers), the differences between "efficiency" of "efficiency" factor is the growth factor.
Price difference = (actual price of input -budget price of input) × actual input quantity The efficiency difference Efficiency difference = (actual input quantity -budget input quantity under actual output) × the budget price of input The main factor is cost. The object of factor analysis is the difference between actual cost and budget cost. There is no efficiency difference, efficiency factors are breeding.  In the original book, the favorable influence of direct materials was undercounted by $2,263.55, while the unfavorable influence of direct materials was overcounted by $2263.55. $1003.74 of adverse effects of labor price was overcounted and $1003.74 of adverse effects of labor quantity was undercounted. The price of materials is the responsibility of the procurement department, the material consumption is the responsibility of the production department, the labor price, labor hours are the matter of labor efficiency, the influence of the total cost of the factor factors affect the difference in the calculation of the wrong amount, which is not only related to the department's responsibility, rights, interests, but also involves the correct attribution of individual responsibility and rights.
In this example, only price and quantity affect the cost, not the so-called "efficiency effect". The factor influence quantity calculated by the exponential logarithmic proportion method fairly divides the interaction between quantity and price, so the answer is different from the traditional factor analysis solution method in the original textbook.
Example 4. Financial analysis by zhang xianzhi and Chen youyou [3]. (8th edition) national planning textbook and national excellent courses for undergraduate students of general higher education during the 12th five-year plan period, published by northeast university of finance and economics press in March 2017, P 170. That is, the influence of the quantity and price of first-class products on sales revenue: 2505.04+1064.96=3570 Influence of quantity and price of second-class goods on sales revenue: -13493.2+1523.21=-11970 The influence of the first and second grades on sales revenue: 3570-11970=-8400 Or the impact of sales volume on sales revenue: 2505.04-13493.21= -10988.17 Influence of price on sales revenue =1064.96+1523.21=

2588.17
The original book answer: the price change to the profit influence 2250 thousand yuan, the rank structure change to the profit influence 1350 thousand yuan, the sale quantity to the profit change influence did not do. If calculated according to the traditional calculation method, the effect of quantity on profit is -12000 thousand yuan, and the total effect is: 3600-12000=-8400. There are only two factors here, sales price and sales quantity. How can we get more "grade structure" factors? Obviously, here, the interaction between sales quantity and sales price is derived into "grade" factors, which is the breeding factor.
Example 5. Financial analysis by zhang xianzhi and Chen youyou (8th edition), national planning textbook and national excellent courses for undergraduate courses of general higher education during the 12th five-year plan period, northeast university of finance and economics press, 2017, p 169-170 2016 product sales profit list unit: thousand yuan Analysis basic equation: sales profit = sales quantity * (unit price -unit cost), or: = sales quantity * unit profit The "structure" factor in the "influence of selling variety structure" is the breeding factor.
The overall impact is 10200= quantity impact 3608.04+ sales variety structure impact 1691.96+ unit price impact 3600-sales cost impact 1300 There is a problem with the original proposition: 1) Repeat conditions are given, either: Total profit = sales quantity × sales unit price -sales quantity × sales cost; Either: total profit = sales volume × unit product profit. The given condition satisfies the double calculation of the two equations.
2) Problem creates a "structural" variable effect that does not exist in the equation. Whether the units of the structure are composite units or ratios; If it's a ratio, it can only be a value ratio, because a single quantity, or unit price, doesn't tell you anything about the structure, so the structure is the value ratio of quantity times unit price, which is a compound variable. There is no "structure" factor in the equation. The "structure" effect calculated by the original problem is only the interaction between the sales volume of different products and the sales price, which is regarded as the influence of the sales product structure. In fact, there are three structures of production (assuming the same production and sales volume), and the cost structure of product varieties and the profit structure of product varieties; In factor analysis they also have a product combination of two factors. The resulting structural effects only complicate simple things.

Calculation Procedures for Normative Factor Analysis
We standardized factor analysis by the following steps: Step 1: establish factor analysis equation; Step 2: calculate the analysis object, i.e. the overall difference of main factors; Step 3: factor factor analysis, list calculation of factor factor influence, factor index logarithmic ratio calculation; Step 4: calculate the difference of factors. Example 6. The relevant knowledge points in the relevant textbooks, using the above method procedures, normative factor analysis at the same time, normative factor analysis steps.
Cost and management accounting (15th edition) by Charles t. gren Srikant m. atar Madhav v. riajan [4] Translated by wang liyan and liu yingwen the first edition of June 2016 by renmin university of China press the 3rd printing of p 464-470 in November 2017 Analyze the differences. Analysis procedures: Step 1: analysis equation: gross profit contribution = gross profit contribution × sales quantity; Step 2: identify the analysis objects (total variance): total actual contribution gross profit -total budget contribution gross profit =3585000-3797500= -212,500 dollars Step 3: factor analysis (factor factor difference analysis) the only two factors that affect the gross profit contributed by the main factors are the gross profit contributed by the unit and the sales volume. However, there are two types of products to be sold: A and B, which need to calculate the difference of influence respectively. Among them "structure" ratio is breeding factor, is redundant. When calculating the difference of product A, the original book wrongly increased the impact of unit contribution gross profit on the total contribution gross profit by $4512.267, and wrongly reduced the impact of product A sales volume on the total contribution gross profit by $4512.267; When calculating the difference between the actual gross profit contribution of product B and the budget, the impact of the gross profit contribution of unit contribution on the gross profit contribution was overcounted, and the impact of the sales volume of product B on the gross profit contribution was undercounted, which was $61444.757. This calculation result will lead managers to misjudge the effect of different products on the contribution of gross profit. Example 7. Financial cost management [5], a textbook for the national unified examination of certified public accountants in 2018, was compiled by the China association of certified public accountants, and published in March 2018 by China financial and economic publishing house, China financial publishing and media group. P 29-30.
"Example 2-1: the actual cost of a certain material used by an enterprise in March 20 X1 is 6,720 yuan, while the planned cost is 5,400 yuan. 1320 yuan more than planned. Because material cost is composed of product output, unit product material quantity and material unit price product product product product product product. Therefore, the total index of material cost can be decomposed into three factors, and then analyze their influence on the total material cost one by one. Now suppose the values of these three factors are shown in Problem solving: 1) Basic equation of analysis: material cost = product output × material consumption × material unit price; 2) Variation difference of material cost of the objects analyzed: 6720-5400=1320 (RMB); 3) Traditional factor analysis balance substitution method.  5) The difference ratio calculated by traditional factor analysis method and exponential logarithmic ratio method. The results of the two methods are compared. The new method changes the difference of the influence of factors on the main factors calculated by the traditional method.
Example 8. Source: cost management accounting by meng yan and liu junyong, national planning textbook for undergraduate courses of general higher education during the 12th five-year plan period, higher education press printed P 109 for the third time in December 2017. The text is omitted [6]. The original book only makes unit change cost impact 13000-unit labor hour consumption impact 6000=7000 (yuan) Compared with the exponential logarithmic ratio method, the difference substitution method has an impact of -599.347 yuan on the total cost difference, the multi-unit variable expense standard has an impact of 1222.367 yuan on the total cost difference, and the multi-hour consumption standard has an impact of 623 yuan on the total cost difference. The original book "variation of manufacturing cost efficiency difference" is actually only "man-hour impact". In this thesis, there are only three factors influencing "product output", "cost of unit labor hour variation" and "unit product labor hour", but no "efficiency" factor. Example 9. Wu xiaoling and tian gaoliang [7] edited the textbook of enterprise financial analysis for 21st century economy and management planning, p 17-19 was printed by Peking University press for the second time in February 2018   1) Analysis equation: total cost = product output × product material consumption × material price 2) Analysis object: 69920-70000=-80 (yuan)

4) exponential logarithmic ratio method
3) Factor analysis (traditional factor analysis, the same as the following table): 4) Factor analysis with exponential logarithmic proportion method  The increase of the total cost by the traditional method is 91.52 yuan. The impact of multiple material prices on total cost reduction was 91.52 yuan. Similarly, the unit consumption of products is the responsibility of the production department, and the price of consuming materials is the responsibility of the procurement department. If the component difference affected by factors is not correct, it will inevitably lead to unclear ownership of the rights and responsibilities of the production department and the procurement department.

5) Methods differences
Example 11. Zhongsheng company USES A material A to produce product A. In this period, the production of 200 products of A consumed 900 kilograms of material A, and the actual price of A was 100 yuan per kilogram. Suppose the standard price of material A is 110 yuan per kilogram, and the material consumption quota of product A is 5 kilograms of material A, then the cost difference of material A is analyzed as follows: Material price difference = (100-110) ×900=-9000 (yuan) Material quantity difference =110× (900-1000) = -11,000 (yuan) Material cost difference =100×900-110×1000= -20,000 (yuan) =-9000+ (-11000) =-20000 (yuan) Source: sun maozhu, zhi xiaoqiang and dai lu, national excellent achievement award, national planning textbook for undergraduate education of general higher education during Example 12. five-year plan, management accounting (8th edition), renmin university of China press [9]. P 215-216. The difference of factor influence between the two calculation methods It indicates that the influence of the material consumption quantity on the cost in the traditional calculation method is overcounted -499.16 yuan, while the influence of price on the cost is undercounted -499.16 yuan. The results of the traditional factor analysis obviously confuse the rights and responsibilities of the purchasing department (material price) and the production department (material consumption).
Example 13. Mr Greg accounting [10]: management accounting booklet (the original book fourth edition) Tracie Nobles, Texas state university at SAN marcos. Brenda Mattison, tri-county technical college; Ella Mae Matsumura, university of Wisconsin, Madison. Zhang yongji et al. Translation machinery industry press January 2017 the first edition. P 266-269, case data text description omitted. The result of traditional calculation method seriously misjudges the responsibility of production department and procurement department in product cost.
Example 14. Data source: Ray h. arrison, Eric w. oreen, Peter c. rewer, 16th Edition, machinery industry press, January 2019, Wang Man [11] translation Management Accounting. P 293. Text data ellipsis. In short, there are many cases of cost difference analysis in management accounting, no longer enumerate.
In the construction of econometrics model, if the elements of the model are in the form of continuous product, the goodness of fit can be effectively improved by increasing the interaction between factors and variables. This is not an example [12][13][14].

Conclusion
To sum up, factor analysis is not only applied to financial accounting, management accounting and cost management accounting; It is also used in textbooks such as "financial cost management", "financial management", "financial analysis" and "applied statistics". Differences in calculation methods of difference analysis in factor product structure of equation structure of factor analysis exist not only in domestic textbooks, but also in several American textbooks. Exist in a lot of performance analysis and evaluation, exist in a lot of cost management analysis, to identify one by one, it is really difficult to enumerate. As the continuity of the article, the end is as follows: 1) In the case of factor product structure, there is interaction between factors. In factor analysis, factor factors are of and difference structure, and there is no interaction between common changes of factors and main factors. The interaction of factors exists only in the product structure.
2) The answer of the traditional factor analysis method is wrong. It mainly refers to the case that the factor structure of factor analysis is the product structure, and the factor difference analysis, the main reason for the error is that the interaction of factors is or omitted. Interaction refers to the difference in the influence of the interaction between factors on the main factors. Such interaction should be fairly Shared among relevant factors and factors. In the analysis and calculation of traditional factors, the difference in the influence of factors should be replaced to occupy the interaction of factors that should be Shared.
3) Factor analysis, exponential logarithmic proportional method, can fairly share the error. In the study of factor analysis and calculation, although some effectively the problems of the interaction research, for many factors are incremental contribution factor interaction factor conditions, but only factor as a special case of the incremental cases, for many factors have increased, many factors as the penalty cases under the interaction of decomposition, remains unresolved. Its problems are common, involving many textbooks, many celebrities and scholars, we can not put the should be able to solve, wrong knowledge is correct inheritance.
4) The results obtained by correct calculation methods shall be regarded as scientific and authoritative. The correct factor analysis results, give the effect of factors on the main factors to be fair, get different experimental differences to analyze the influence of factors; To give the rights and responsibilities of different factors to be clear; It provides a basis for the accurate adjustment of factor quantity in future successful experiments.
Limited by space, the above books related factors analysis of the difference analysis of many cases, this paper is no longer enumerating; There are also "statistics", "auditing" and other textbooks with the same above problems, this article will not repeat. Finally, thank you to Judy Garland for your warm, patient, and thoughtful guidance.

Appendix
Noun Shorthand