Chapter 8, Problem 42C

1.

To determine

Prepare an operating income statement of Company L for both years under absorption costing method.

Explanation of Solution

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”.

Prepare an operating income statement of Company L for both years under absorption costing method as follows:

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 (1)

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 (2)

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.

2.

To determine

Prepare an operating income statement of Company L for both years under variable costing method.

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.

Prepare an operating income statement of Company L for both years under variable costing method as follows:

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 (3)

Working note (4):

Calculate the cost of ending inventory for year 1:

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

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

3.

To determine

Reconcile the operating income reported under variable and absorption costing for year 1 and year 2.

Explanation of Solution

Reconcile the operating income reported under variable and absorption costing for year 1 and year 2as follows:

Year 1:

$\begin{array}{c}\begin{array}{l}\text{Differene in the }\\ \text{reported income }\end{array}\}\text{= }\left(\begin{array}{l}\left(\text{Production units}-\text{Sales units}\right)\times \\ \text{Predetermined fixed overhead rate per unit}\end{array}\right)\\ =\left(3,000\text{ units}-2,500\text{ units}\right)\times \text{\$14 per unit (5)}\\ \text{=\$7,000}\end{array}$

In this case, the operating income of Company L is higher under absorption costing, because the production units (3,000 units) are more than the sales units (2,500 units), and under absorption costing the fixed overhead is inventoried until when the manufactured goods are sold. Hence, the fixed overheads for 5,000 $\left(3,000\text{ units }-2,500\text{ units}\right)$ units are not considered to determine the operating income under absorption costing. When the production units are more than the sales units, then the operating income under absorption costing ($27,500) should be more than the variable costing ($20,500).

Working note (5):

Calculate the predetermined fixed overhead rate.

$\begin{array}{c}\text{Fixed overhead rate per unit = }\frac{\text{Fixed overhead manufacturing overhead}}{\text{Production units}}\\ =\frac{\$42,000}{3,000\text{ units}}\\ =\$14\text{ per unit}\end{array}$

Year 2:

$\begin{array}{c}\begin{array}{l}\text{Differene in the }\\ \text{reported income }\end{array}\}\text{= }\left(\begin{array}{l}\left(\text{Production units}-\text{Sales units}\right)\times \\ \text{Predetermined fixed overhead rate per unit}\end{array}\right)\\ =\left(2,000\text{ units}-2,500\text{ units}\right)\times \text{\$14 per unit (5)}\\ \text{=(\$7,000)}\end{array}$

In this case, the operating income of Company L is higher under variable costing, because the fixed overhead under variable costing is calculated only for current year production units (2,000 units), and the changes in the production and sales units is not consider. But in the absorption costing, the fixed overhead incurred in the prior year (500 units of inventory) increases the current year fixed overhead and the fixed overhead under absorption costing is comparatively higher than the variable costing. Hence, when the production units are less than the sales units, then the operating income ($20,500) under variable costing should be higher than the absorption costing ($13,500).