http://www11.plala.or.jp/yuichiro-h/, (c) Aug. 2003, Yuichiro Hayashi

5-2. Income statement and managed gross profit

An income statement under absorption costing of a manufacturing company will be the object to be studied. The management accounting departments of the company shall be comprised of: (a) a manufacturing direct cost department, (b) a manufacturing overhead department, (c) a selling and general administrative expenses department, and (d) a profit and loss summary department. Each department can be divided further into smaller accounting sections.

Let the symbol X represent sales. It is assumed that manufacturing costs consist of manufacturing direct cost D (actual and variable cost) and manufacturing overhead C (actual cost). Manufacturing overhead is also replaced by manufacturing indirect cost. Selling and general administrative expenses (SG&A expenses, actual costs) are period costs and denoted as the symbol G. The term of indirect costs means the sum of manufacturing overhead and SG&A expenses. Operating profit is denoted as the symbol P. The costs C and G are not necessarily defined to be constant. Applied manufacturing overhead allocated from C is denoted as the symbol A. Any basis of manufacturing overhead allocation is allowable as far as it is applied to practical accounting.

When inventory assets exist, cost of goods sold and cost of goods manufactured should be classified separately from each other. Then the superscript X is added to any cost as in A^X, when it belongs to cost of goods sold. The superscript Y is added to any cost as in A^Y, when it belongs to cost of goods manufactured.

Again, costs should be classified whether they belong to inventories or not. Then superscripts (−) and (+) are added to the costs incurred belonging to the year-beginning inventories and the year-ending inventories, respectively, in a fiscal period. The superscript (0) is added to the costs incurred, which do not belong to the inventories in the current period.

When inventories exist, manufacturing direct costs are directly charged to both goods sold and inventory costs. Also, manufacturing overhead costs are allocated to the two costs. In standard costing, standard cost are normally adopted in both manufacturing direct cost and manufacturing overhead. However, it is assumed, for simplicity of description in this paper, that standard cost is adopted only in the allocation of manufacturing overhead. Any allocation basis of manufacturing overhead is allowed as far as manufacturing overhead costs in inventories are valuated only by the standard cost. Cost variance is regarded as period cost.

One of purposes in management accounting is presenting managerial accounting data, which are needed for company managers. In those data, a forecasted or budgeted income statement is very important at the beginning of a fiscal year. A forecasted income statement at the beginning will be continuously revised to each new following statement to arrive at the final statement according to progress of managerial activity. Consequently, there are many kinds of forecasted income statements including the final statement in management accounting. Furthermore, break-even analysis is a theoretical approach in the case where the final sales in the final statement are different from the final sales. Therefore it is needed to distinguish whether accounting data belong to the final data or to the forecasted data.

The symbol (ε) is added to any symbol when the symbol means accounting data on the final statement, and the symbol (ρ) is added to any symbol when the symbol means data on forecasted statements. The symbol (ε) or (ρ) is taken off when the original symbol represents coordinate axes or a variable.

Final financial statements, of a manufacturing company, which are for operating income and under absorption costing, are shown in Table 1 and Table 2.



Table 1 Income statement-1

Item	Debit	Credit
Sales		X (ε)
Manufacturing direct cost	D^X (ε)=D^{X (-)} (ε) + D^{X (0)}(ε)
Manufacturing overhead	A^{X (−)} (ε) + C (ε) - A^{Y (+)} (ε)
SG&A expenses	G (ε)
Operating profit	P (ε)



Table 2 Balance sheet (Inventories)

Item	Debit	Credit
Beginning Inventory	D ^{X (-)} (ε) + A^{X (-)} (ε)	D^{X (-)} (ε) + A^{X (-)} (ε)
Ending Inventory	D^{X (+)} (ε)+ A^{X (+)} (ε)

Relationships between manufacturing overhead applied in goods sold and inventories are shown in Fig. 1.

Manufacturing overhead applied in cost of goods sold		Manufacturing overhead applied in cost of ending Inventory
A^X (ε)
A^{X (-)} (ε)	A^{X (0)}(ε)= A ^Y(0)(ε)	A^{Y (+)}(ε)
	A^Y(ε)
Manufacturing overhead applied in cost of beginning inventory	Manufacturing overhead applied in cost of goods manufactured

Fig.1 Maｎｕｆａｃｔｕｒｉｎｇｏｖｅｒｈｅａｄａｐｐｌｉｅｄｉｎｇｏｏｄｓｓｏｌｄａｎｄｉｎｖｅｎｔｏｒｉｅｓ



In Fig. 1, the symbol η (ε) is defined as follows:
η (ε) = A^X (ε) - A^Y (ε)
= A^{X (-)} (ε) - A^Y(+)(ε)	(1)
By using Eq. (1), Table 1 is converted to Table 3.

Table 3　 Income statement-2

Item	Debit	Credit
Sales		X (ε)
Manufacturing direct cost	D^X (ε)
Manufacturing overhead	A^X(ε)
Cost variance	C (ε) - A^Y(ε)
SG&A expenses	G (ε)
Operating profit	P (ε)


If sales gross profit is shown as the symbol Q (ε) and cost variance in manufacturing overhead department is shown as the symbol δ (ε) in Table 3, the following equations are obtained:
δ (ε) = C (ε) - A^Y(ε)
= C (ε) - ( A^X(ε) - η (ε) )	(2)
Q (ε) = X (ε) - ( D^X (ε) + A^X(ε) +δ (ε) )
= X (ε) - D^X (ε) - (C (ε) +η (ε) )	(3)
P (ε) = Q (ε) - G (ε)	(4)

Here, the symbol Q^M(ε) is defined as follows:
Q^M(ε) = X (ε) - D^X(ε) - A^X(ε)	(5)

The symbol Q^M(ε) is a concept corresponding to sales gross profit Q (ε) when manufacturing overhead is temporarily calculated by using manufacturing overhead applied A^X(ε) in place of the actual manufacturing overhead ( C (ε) + η (ε) ) or (A^X(ε) +δ (ε) ). The symbol Q^M(ε) is termed ‘managed gross profit’ in this paper.

From Eq. (3), Eq. (4) and Eq. (5), the following equations are obtained:
Q (ε) = Q^M (ε) - δ (ε)	(6)
P (ε) = Q (ε) - G (ε)
= Q^M(ε) - δ (ε) - G (ε)
=Q^M(ε) +A^X(ε) - C (ε) - η (ε) - G (ε)	(7)