Chapter 8, Problem 44C

1.

To determine

Explain the reason why the ending balance of finished goods inventory for year 1 is higher if company L is using absorption costing and variable costing.

Explanation of Solution

Variable Costing: Managers frequently use variable costing for internal purposes for taking decision making. The cost of goods manufactured includes direct materials, direct labor, and variable factory overhead. Fixed factory overhead treated as period (fixed) expense.

Absorption Costing: “Absorption costing is a method that allocates “direct labor, direct materials, fixed manufacturing overhead and variable manufacturing overhead” to products and it is required by GAAP for the purpose of external reporting”.

Explain the reason why the finished goods inventory for year 1 is higher if company L is using absorption costing and variable costing as follows:

Company L has 500 units $\left(3,000\text{ units}-2,500\text{ units}\right)$ finished goods inventory for year 1. In this case, the ending balance of finished goods inventory for year 1 is higher under absorption costing because the fixed manufacturing cost is a product cost and the fixed manufacturing cost is included in the inventory cost under absorption costing. Hence, the balance of finished goods inventory is higher under absorption costing than the variable costing. Whereas, under variable costing the fixed manufacturing cost is not included in the inventory cost because under variable costing, only period costs are included in the inventory cost.

2.

To determine

Explain the reason why the ending balance of finished goods inventory for year 2 is same under both absorption and variable costing.

Explanation of Solution

Explain the reason why the ending balance of finished goods inventory for year 2 is same under both absorption and variable costing as follows:

The ending balance of finished goods inventory for year 2 is same under both absorption and variable costing because company L has no finished goods inventory on hand at the end of the year 2. In this case, the total production units for two year $\left(2,500\text{ units + 2,500 units}\right)$ are equal to the total sales units $\left(3,000\text{ units + 2,000 units}\right)$. Hence, the ending balance of finished goods inventory for year 2 is same under both absorption and variable costing.

3.

To determine

Explain whether the given relationship between the absorption and variable costing will always true at any balance sheet date.

Explanation of Solution

Explain whether the given relationship between the absorption and variable costing will always true at any balance sheet date as follows:

Yes, this relationship will always true at any balance sheet date, because the cost of inventory under absorption costing will be higher than the inventory cost measured under variable costing. Under absorption costing, the fixed manufacturing overhead is inventoried as a product cost, whereas under variable costing, the fixed manufacturing overhead is not inventoried as a product cost, instead it is treated as a period costs and expensed during the period in which it is incurred.

4.

To determine

Calculate the declined amount of finished goods inventory during year 2 under absorption costing and variable costing.

Explanation of Solution

Calculate the declined amount of finished goods inventory during year 2 under absorption costing and variable costing as follows:

Particulars	Finished-Goods Inventory
	End of Year 1 (A)	End of Year 2 (B)	Amount of Decline $\left(A-B\right)$
Absorption costing	$ 10,500	$ 0	$ 10,500
Variable costing	$ 3,500	$ 0	$ 3,500

Table (1)

5.

To determine

Calculate the difference in the amount of declined finished goods inventory under absorption and variable costing, calculate the difference in the reported operating income for year 2 under absorption and variable costing, and compare both differences.

Explanation of Solution

Calculate the difference in the amount of declined finished goods inventory under absorption and variable costing:

Particulars	The decline amount of finished goods during year 2
Absorption costing	$ 10,500
Less: Variable costing	$ 3,500
Difference	$ 7,000

Table (2)

Calculate the difference in the reported operating income for year 2 under absorption and variable costing:

Particulars	Reported operating income for year 2
Absorption costing  (5)	$ 13,500
Less: Variable costing  (6)	$ 20,500
Difference	-$ 7,000

Table (3)

Working note (1):

Calculate the value of sales revenue for both years.

Particulars	Production units (A)	Year 1 $\left(A\times 50\text{ per unit}\right)$	Year 2 $\left(A\times 50\text{ per unit}\right)$
Sales revenue	2,500 units	$15.00	$1,875,000

Table (4)

Working note (2):

Calculate the cost of goods manufactured for both years.

Year 1:

$\begin{array}{c}\text{Cost of goods manufactured =}\left[\begin{array}{l}\text{Variable manufacturing costs}\text{+}\\ \text{Fixed manufacturing overhead}\end{array}\right]\\ =\$21,000+\$42,000\\ =\$63,000\end{array}$

Year 2:

$\begin{array}{c}\text{Cost of goods manufactured =}\left[\begin{array}{l}\text{Variable manufacturing costs}\text{+}\\ \text{Fixed manufacturing overhead}\end{array}\right]\\ =\$14,000+\$42,000\\ =\$56,000\end{array}$

Working note (3):

Calculate the cost of ending inventory for year 1:

$\begin{array}{c}\text{Ending inventory cost = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Production units}-\\ \text{Sales units}\end{array}\right)\times \\ \frac{\text{Cost of goods avaiable for sales}}{\text{Production units}}\end{array}\right]\\ =\left[\left(3,000\text{ units }-2,500\text{ units}\right)\times \frac{\$63,000}{3,000\text{ untis}}\right]\\ =\$10,500\end{array}$

Note: The ending inventory for year 1 is considered as the beginning inventory for year 2.

Working note (4):

Calculate the cost of ending inventory for year 1:

$\begin{array}{c}\text{Ending inventory cost = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Production units}-\\ \text{Sales units}\end{array}\right)\times \\ \frac{\text{Cost of goods avaiable for sales}}{\text{Production units}}\end{array}\right]\\ =\left[\left(3,000\text{ units }-2,500\text{ units}\right)\times \frac{\$21,000}{3,000\text{ untis}}\right]\\ =\$3,500\end{array}$

Working note (5):

Calculate the operating income under absorption costing.

Operating income statement under absorption costing method
Particulars	Year 1	Year 2
Sales revenue (1) (C)	$ 125,000	$ 125,000
Less: Cost of goods sold:
Beginning finished-goods inventory (3)	$ 0	$10,500
Cost of goods manufactured  (2)	63,000	56,000
Cost of goods available for sale	$63,000	$66,500
Ending finished-goods inventory  (3)	10,500	$ 0
Cost of goods sold  (D)	$52,500	$66,500
Gross margin  $\left(C-D\right)$	$72,500	$58,500
Less: Selling and administrative expenses	$ 45,000	$ 45,000
Operating income	$27,500	$13,500

Table (5)

Working note (6):

Calculate the operating income under variable costing.

Particulars	Year 1	Year 2
Sales revenue  (E) (1)	$ 125,000	$ 125,000
Less: Cost of goods sold:
Beginning finished-goods inventory	$ 0	$3,500
Cost of goods manufactured	21,000	14,000
Cost of goods available for sale	$21,000	$17,500
Ending finished-goods inventory (4)	$3,500	$0
Cost of goods sold	$17,500	$17,500
Add: Variable selling and administrative costs	$25,000	$25,000
Total variable costs (F)	$42,500	$42,500
Contribution margin  $\left(E-F\right)$	$82,500	$82,500
Less: Fixed costs:
Manufacturing	$42,000	$42,000
Selling and administrative	$20,000	$20,000
Total fixed costs	$62,000	$62,000
Operating income	$20,500	$20,500

Table (6)

6.

To determine

Explain whether the given relationship between the absorption and variable costing will always true at any balance sheet date.

Explanation of Solution

Explain whether the given relationship between the absorption and variable costing will always true at any balance sheet date as follows:

Yes, this relationship will always true at any balance sheet date. There are two ways to explain this issue.

1. Based on theoretical: The value of inventory increase the reported operating income under absorption costing than variable costing, because the fixed manufacturing cost is a product cost and the fixed manufacturing cost is included in the inventory cost under absorption costing. Hence, the balance of finished goods inventory is higher under absorption costing than the variable costing. Whereas, under variable costing the fixed manufacturing cost is not included in the inventory cost because under variable costing, only period costs are included in the inventory cost.

The retained earnings are the total of net operating income of the company across its entire life. The company cannot sell more units than it ever produced. Hence, the inventory balance of the company cannot decrease and either it will remain at zero or increased. Therefore, the retained earnings reported under absorption costing will be greater (or same) than the retained earnings reported under variable costing.

2. Based on the accounting equation:

$\begin{array}{l}\text{Assets}\\ \uparrow \text{Increase in inventory}\text{(I)}\end{array}\}\text{ = Liabilities + }\left\{\begin{array}{l}\text{Owner's equity}\\ \uparrow \text{Increase in retained earnings (RE)}\end{array}\right\}$

${\text{I}}_a\ge {\text{I}}_v={\text{RE}}_a\ge {\text{RE}}_v$

Note: a = absorption costing, v = variable costing, I = inventory and RE = retained earnings.

The elements that are affected in the accounting equation are inventory (I) and retained earnings (RE). When the inventory is greater under absorption costing, then the owner’s equity must be higher under abortion costing.