Overview of the US Patent, 2013: Accounting Method and Accounting System

 

A new marginal profit chart which unifies management accounting and financial accounting under standard costing

April 28, 2014 Hayashi, Yuichiro   Doctor of Engineering

Hayashi, Yuichiro Pres. YOU-SHOJI, Ltd. in Japan is proud to announce the issuance of US patent, entitled “Accounting method and accounting system", No. US 8,554,646 B2, Oct. 8, 2013. The following presents an overview of the patented method. 

■ 2013 Profit Chart and 2007 Profit Chart under Standard Costing

The break-even chart under standard costing (hereinafter referred to as the profit chart) utilized in the US Patent in 2013 is shown in Figure 1 (2013 Profit Chart). Figure 1 is closely associated with the US patent entitled “Accounting system for absorption costing”, NO. US 7,302,409 B2, Nov. 27, 2007. The profit chart used in the US patent in 2007 is shown in Figure 2 (2007 Profit Chart). At the stage of the patent 2007, π^O was not yet divided into π^MO and π^AC; this was created in a subsequent study by the inventor.

　

Figure 1. 2013 Profit Chart

Figure 2. 2007Profit Chart

■ Financial Accounting and Management Accounting

Business accounting is divided into financial accounting and management accounting. Financial accounting is a method that makes financial statements in accordance with cost accounting standards in order to report those to external parties such as tax authorities and shareholders. Management accounting is freely executed for internal company members to report a company’s profit planning and present profit performance to managers; to make cost estimates based on manufacturing costing accounting. From a viewpoint of ideal management accounting, its method should enable monthly or even weekly profit management on each job site as a profit center; the profit should be determined in accordance with cost accounting standards. For that reason, management accounting should be easy to understand and executed swiftly and correctly, therefore a profit chart is essentially indispensable in any management accounting situation.

■ Standard Costing

Manufacturing product costs are comprised of variable costs or manufacturing direct costs (direct materials, direct labor, direct overhead); and fixed costs or manufacturing overhead costs (indirect materials, indirect labor, depreciation and others); the total of the variable and the fixed costs is called the manufacturing absorption cost. Cost accounting is a method that determines manufacturing product costs incurred for a single unit of product; it is divided into standard costing and direct costing. Standard costing is said to have originated in England around 1870, during the later stages of the industrial revolution. Early twentieth century, Alexander Hamilton Church, US engineer and accountant proposed a prototype of the present standard costing, which has had a great effect on official costing accounting standards. In standard costing, a normal price consisting of variable and fixed costs for a single product is predetermined as a manufacturing absorption cost; multiplying the normal unit prices by actual product quantities gives the manufacturing absorption cost under standard costing.

■ Operating profit under Standard Costing

In standard costing, we determine the operating profit at the end of the final year as the result of the following process. Let X be “Sales or Goods sold”; Q be “Sales gross profit”; π^O be “Sales operating profit”; D^X be “Manufacturing direct cost (variable and actual) ”; C be “ Manufacturing overhead cost (fixed and actual) ”; G be “Selling and administrative costs (fixed and actual) ”; E be “ Manufacturing absorption cost”; A^CX be “Manufacturing overhead allocation cost to X”; A^CY be “Allocation revenue of C accounting department during the present accounting period”; A^{CY( + )} be “Year-ending A^CY carried forward to inventories”;  A^{CX( - )} be “Year-beginning A^CX carried down to X”. η (eta) = A^CX(-) - A^CY(+) = A^CX - A^CY is named “Net carryover manufacturing overhead allocation cost”. Operating profit π^O is obtained as follows. : Q = X – E; E = D^X + C + A^{CX( - )} - A^{CY( + )} = D^X + [C + η]; π^O = Q – G = X - D^X - [C + η + G] ·····(1). Eq. (1) shows that the amount of η affects the value of π^O. 

■ Direct Costing

 In the movement that standard costing was being officially adopted, in the US in 1936, Jonathan N. Harris pointed out drawbacks in standard costing and stressed the superiority of direct costing as an internal management accounting tool. Direct costing is a method where; C is treated as a fixed, period cost like the selling and administrative costs. Using the notations V^D = X - D^X and F^D = C + G gives π^O = V^D - F^D, where F^D is a constant. If in Figure 1 we let η = 0 and A^CX =0, we obtain the direct costing profit chart or the marginal profit chart. In the figure, F^D is drawn as a horizontal line. The drawbacks of this method are that standard costing is complicated, for example, in the cases of contract negotiations, paying taxes and offering internal management accounting reports; on the other hand, direct costing is very simple and additionally its profit chart can be utilized. We also have “direct standard costing” but its explanation is left out. It seems that such cost accounting methods, unifying financial costing and management costing have been increasingly demanded.

 ■ 2007 Profit Chart

The inventor was involved in a construction company manager for many years, when, in 1995, he felt a desire to construct an accounting system where both management accounting and financial accounting directly correlated to each other; the accounting reports would be transferred to each job site through a local area network system with PC. The inventor began the study to draw a profit chart for standard costing. As a result, the inventor created the profit chart shown in Figure 2, and the accounting method using the chart was awarded a patent by the USPTO in 2007. Its contents is as follows.

For management accounting under standard costing, besides the above-mentioned notations, we define the following accounting technical terms and notations at any given point in time during a year accounting period, e.g. a monthly or even weekly ending. Let E^M = D^X + A^CX be “Managed manufacturing absorption cost”; Q^M = X - E^M be “Managed gross profit”; π^MO = Q^M - G be “Managed operating profit”; π^AC = A^CX - (C + η) be “Managed allocation profit” or “Managed manufacturing overhead allocation profit”; δ = A^CY - C be “Manufacturing overhead variance”; V^S = X - D^X be “Marginal profit”; F^S = C + η + G be “Managed fixed cost”. Using those notations, we obtain Figure 2 expressing the locus of the marginal condition where π^O = 0 is satisfied in Eq. (1). Observing Figure 2 gives π^O = π^MO + π^AC and π^AC = A^CX - (C + η). Since η = A^CX + A^CY, we can also express π^AC = δ. Since none of the formal terms had existed in conventional accounting, the inventor coined these for management accounting.

■ 2013 Profit Chart

From the view point of the inventor, the 2007 Profit Chart was superior to the direct costing profit chart in the management accounting area. The direct costing profit chart has a single value of π^O but the 2007 Profit Chart has two vales of π^MO and π^AC independent of each other. In management accounting, π^MO shows an operating profit of sales-departments and π^AC indicates an allocation profit of manufacturing-overhead-departments. Practically speaking, π^AC is a profit and loss, in relation to a capacity variance; this is affected by enhancing capacity utilization and economic fluctuation. Therefore, we can establish sharing of profit responsibility between manufacturing and sales departments; investigating the cause of a loss and deciding a proper size of capital investment.

The inventor was stressing to the employees that managed fixed cost F^S including η shown in Fig.2 is a constant. However, the marginal gross profit ratio line (segment EN), which should connect with F^S is an oblique line from top left to bottom right. Since such a profit chart has not been taught in accounting education, the more educated members in accounting feel disinclined to use the 2007 Profit Chart. Therefore, the inventor began to research how to draw the line F^S horizontally in Figure 2.

One day, an idea of transforming Figure 2 to Figure 1 occurred to the inventor and it was verified as follows: π^O = π^MO + π^AC = Q^M - G + A^CX - (C + η) = [Q^M + A^CX] - [C + η + G] ····· (2). From Eq. 1 we have V^S = X - D^X = π^O + [C + η + G] ····· (3). From Eq. 2 and Eq. 3 we obtain V^S = Q^M + A^CX. Substituting V^S into Eq. (2) gives π^O = V^S - F^S. Consequently, Figure 1 and Figure 2 are equivalent to each other, therefore Figure 2 also includes the marginal profit chart under direct costing. However, the latter chart cannot be divided to express π^O as the separate values of π^MO and π^AC. We can easily transform Figure 1 into a 45 degree line break-even chart which is equivalent to Eq. (1).

At any point in time of management accounting, if we determine A^CY(+) in the C accounting departments, π^O derived using the technical terms of management accounting items defined here is always equal to π^O defined in financial accounting. When you look at Figure 1 after the inventor’s creations of both Figure 2 and Figure 1, you might think that inventor easily and previously could have created Figure 1; but if the inventor had not created Figure 2 previously, the inventor probably could not have done Figure 1 afterward. 　

■ Utilization of 2013 Profit Chart

By virtue of the present invention, we have the two charts of 2013 and 2007. From the characteristics of the charts, we can separately use the charts in such a way as we use the 2013 Profit Chart for social accounting education, internal company training and making a company’s profit plan; and use the 2007 Profit Chart for practical cost accounting which connects each profit center’s management accounting with the head office’s financial accounting. We can further obtain the π^MO chart and the π^AC chart independent of each other. In addition, the technical term “profit center” whilst maintaining its original function includes a cost center and an investment center. 

■ Choosing a Cost Accounting System

Eq. (1) is the equation formally used in financial accounting under standard costing. If we let the i-th accounting period be denoted subscript i, so that we have Σ₁ⁿ π^O_i = Σ₁ⁿ [X_i - (D_i + C_i + G_i) ] - A₁^{CX( - )} + A_n^{CY( + )} ]. If we let A₁^{CX( - )} = A_n^{CY( + )} = 0 in the equation at the start and the closure of a company, we have cumulative π^O = cumulative sales amount + cumulative actual costs. Therefore, as far as the tax payment amount for the all accounting periods, it is possible to choose either method cost accounting. 

However, standard costing enables us to determine the manufacturing costs per a single unit of product more correctly including both manufacturing direct and overhead costs. Then in the case of producing a wide variety of products (or running many job site businesses) in a company, standard costing shows us the profit at each cost center more simply, swiftly, correctly and in a visualized manner; further, the cost information of π^MO and π^AC are effectively utilized. The method of allocating the actual costs, incurred at the C accounting departments, to each profit center is described in the 2007 patent specification. 

■ Break-even point formulae under standard costing

From Figure 1, we have π^O = Q^M + A^CX – F^S = (tanα + tanβ) X - F^S, where tanα = A^CX / X (a manufacturing overhead allocation cost ratio) and tanβ = Q^M/ X (a managed gross profit ratio). Since the break-even point sales amount is X satisfying π^O = 0, when the sales amount is denoted by X (χ), the following formula is obtained: X (χ) = F^S / (tanα + tanβ) ·····(4) . Further, since V^S = X - D^X, we can easily obtain tanα + tanβ + tanγ = 1·····(5), where tanγ = D^X / X (a variable cost ratio), so that we can also have another formula X (χ) = F^S / (1 – tanγ) ·····(6). Eq. (6) substituted η = 0 and A^CX = 0 is equal to the conventional break-even point formula in direct costing, Therefore, the two formulae Eq.(4) and Eq. (6) are the break-even point ones under standard costing extended from the direct costing. In addition, the inventor firstly proposed Eq.(6) in the 2007 patent specification by pointing out an error in Solomons’ theory. 

■ Fundamental advantages of standard costing

The first advantage in standard costing is that Figure 2 shows that "π ^O consists of π ^AC and π ^MO“. The second one is that π^O does not vary in proportion to tanβ but does as a function of variables [tanα + tanβ]; tanα is nearly-constant to similar products and tanβ shows selling departments’ profit performance. 

■ Significance of the Patent

(1) Break-even charts and a break-even formula have been said that these should be applied to merely the final profit statement; therefore these might have been treated as displays on accounting textbooks. However, according to these patents, π^O calculated by using management accounting technical terms data always equal π^O under financial accounting by the aid of π^AC.

Thus, it is very useful for a company to use this accounting method in order to manufacture a wide variety of products where each product’s accounting is treated as a profit center. The outstanding problem for many decades concerning the difference between standard costing and direct costing profit charts is now solved. This means that both standard costing and direct costing are unified. 

(2) Since financial accounting and management accounting are entirely-different accounting systems, they are comprised of different data sets. The accounting method of these patents enables these two data sets to be connected through the help of π^AC. Consequently, this patent will become a starting point over the coming decades in order to develop new management accounting methods. 

(3) When it comes to academic significance in accounting, the inventor found that η = A^CX(-) - A^CY(+) = A^CX - A^CY can be treated as a fixed cost in accounting analyses regardless of the fact that both A^CX and A^CY are individual functions of sales X. 

■ References

References are listed in the 2007 Patent specification.