Chapter 8, Problem 43C

Refer to the information given in the preceding case for Lehighton Chalk Company.

Required:

1. 1. Reconcile Lehighton’s operating income reported under absorption and variable costing, during each year, by comparing the following two amounts on each income statement:
   • Cost of goods sold
   • Fixed cost (expensed as a period expense)
2. 2. What was Lehighton’s total operating income across both years under absorption costing and under variable costing?
3. 3. What was the total sales revenue across both years under absorption costing and under variable costing?
4. 4. What was the total of all costs expensed on the operating income statements across both years under absorption costing and under variable costing?
5. 5. Subtract the total costs expensed across both years [requirement (4)] from the total sales revenue across both years [requirement (3)]: (a) under absorption costing and (b) under variable costing.
6. 6. Comment on the results obtained in requirements (1), (2), (3), and (4) in light of the following assertion: Timing is the key in distinguishing between absorption and variable costing.

To determine

Reconcile the reported operating income of company L for each year under absorption and variable costing, by comparing the cost of goods sold and fixed cost on each income statement.

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”.

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.

Reconcile the reported operating income of company L for each year under absorption and variable costing as follows:

For year 1:

Figure (1)

For year 2:

Figure (2)

Working note (1):

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 (2) (C)	$ 125,000	$ 125,000
Less: Cost of goods sold:
Beginning finished-goods inventory (4)	$ 0	$10,500
Cost of goods manufactured  (3)	63,000	56,000
Cost of goods available for sale	$63,000	$66,500
Ending finished-goods inventory  (4)	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 (2):

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	$125,000	$125,000

Table (2)

Working note (3):

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 (4):

Calculate the cost of ending inventory for year 1:

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

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

Working note (5):

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 (6)	$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 (6):

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.

Under the fixed cost for year 1 only the selling and administrative cost are consider.

To determine

Ascertain the total operating income of company L for both years under absorption costing and under variable costing.

Explanation of Solution

Ascertain the total operating income of company L for both years under absorption costing and under variable costing as follows:

Total operating income under absorption costing:

$\begin{array}{c}\begin{array}{l}\text{Total operating income}\\ \text{under absorption costing}\end{array}\}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Operating income under }\\ \text{absorption costing for year 1}\end{array}\right)\\ +\left(\begin{array}{l}\text{Operating income under}\\ \text{absorption costing for year 2}\end{array}\right)\end{array}\right]\\ =\text{\$27,500 (1)}+\text{\$13,500 (1)}\\ =\$41,000\end{array}$

Total operating income under variable costing:

$\begin{array}{c}\begin{array}{l}\text{Total operating income}\\ \text{under variable costing}\end{array}\}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Operating income under }\\ \text{variable costing for year 1}\end{array}\right)\\ +\left(\begin{array}{l}\text{Operating income under}\\ \text{variable costing for year 2}\end{array}\right)\end{array}\right]\\ =\text{\$20,500 (5)}+\text{\$20,500 (5)}\\ =\$41,000\end{array}$

To determine

Ascertain the total sales revenue of company L both years under absorption costing and under variable costing.

Explanation of Solution

Ascertain the total sales revenue of company L both years under absorption costing and under variable costing as follows:

Total sales revenue under absorption costing:

$\begin{array}{c}\begin{array}{l}\text{Total sales revenue}\\ \text{under absorption costing}\end{array}\}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Sales revenue under }\\ \text{absorption costing for year 1}\end{array}\right)\\ +\left(\begin{array}{l}\text{Sales revenue under}\\ \text{absorption costing for year 2}\end{array}\right)\end{array}\right]\\ =\text{\$125,000 (2)}+\text{\$125,000 (2)}\\ =\$250,000\end{array}$

Total sales revenue under variable costing:

$\begin{array}{c}\begin{array}{l}\text{Total sales revenue}\\ \text{under variable costing}\end{array}\}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Sales revenue under }\\ \text{variable costing for year 1}\end{array}\right)\\ +\left(\begin{array}{l}\text{Sales revenue under}\\ \text{variable costing for year 2}\end{array}\right)\end{array}\right]\\ =\text{\$125,000 (2)}+\text{\$125,000 (2)}\\ =\$250,000\end{array}$

To determine

Ascertain the total of all costs expensed on the operating income statements of company L for both years under absorption costing and under variable costing.

Explanation of Solution

Total of all costs expensed under absorption costing:

$\begin{array}{c}\begin{array}{l}\text{Total of all costs expensed}\\ \text{under absorption costing}\end{array}\}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Cost of goods sold}+\text{Selling and}\\ \text{administrative expenses for year 1}\end{array}\right)(1)\\ +\left(\begin{array}{l}\text{Cost of goods sold}+\text{Selling and}\\ \text{administrative expenses for year 2}\end{array}\right)(1)\end{array}\right]\\ =\left(\text{\$52,500}+\text{\$45,000}\right)+\left(\text{\$66,500}+\$45,000\right)\\ =\$97,500+\$111,500\\ =\$209,000\end{array}$

Total of all costs expensed under variable costing:

$\begin{array}{c}\begin{array}{l}\text{Total of all costs expensed}\\ \text{under variable costing}\end{array}\}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Total variable cost}+\text{Total}\\ \text{fixed costs for year 1}\end{array}\right)(5)\\ +\left(\begin{array}{l}\text{Total variable cost}+\text{Total}\\ \text{fixed costs for year 2}\end{array}\right)(5)\end{array}\right]\\ =\left(\text{\$42,500}+\text{\$62,000}\right)+\left(\text{\$42,500}+\$62,000\right)\\ =\$104,500+\$104,500\\ =\$209,000\end{array}$

To determine

Deduct the total costs expensed from the total sales revenue of company L for both years (a) under absorption costing and (b) under variable costing.

Explanation of Solution

a. Deduct the total costs expensed from the total sales revenue of company L for both years under absorption costing as follows:

$\begin{array}{c}\text{Absorption costing}=\left[\text{Total sales revenue}-\text{Total costs expensed}\right]\\ =\$250,000-\$209,000\\ =\$41,000\end{array}$

b. Deduct the total costs expensed from the total sales revenue of company L for both years under variable costing as follows:

$\begin{array}{c}\text{Variable costing}=\left[\text{Total sales revenue}-\text{Total costs expensed}\right]\\ =\$250,000-\$209,000\\ =\$41,000\end{array}$

To determine

Evaluate the results of the above calculation.

Explanation of Solution

• In this case, the company has sold same number of (2,500) units for both years, at a price of $50. Therefore, the total sales revenue is same for both years under absorption and variable costing and sales revenue has nothing to do with the costing method used.
• The total costs expensed ($209,000) for both years are also same under variable and absorption costing. Because the company has sold the same number of units for both years.
• The combined operating income of Company L for the two-year period is $41,000 under both absorption and variable costing. Because the total sales revenue and the total expenses of the company are same under both costing methods over the two-year.
• The analysis in requirement (1) indicates that the operating income of company L is distributed differently for both years under absorption and variable costing. Therefore, the operating income under the two costing methods is not the same within each year. Under absorption costing, the operating income is higher by $7,000 for year 1 and for year 2 it is lower by $7,000. Because the expenses under absorption costing are $7,000 lower in year 1 and $7,000 greater in year 2. However, it reported the same operating income across the two-year combined period under both costing methods.
• Therefore, the difference between absorption and variable costing is caused by the timing with which expenses are recognized. For instance: Under absorption costing, the fixed manufacturing overhead is not expensed until year 2. Whereas, under variable costing all of the fixed manufacturing overhead is expensed in year 1 as a period cost.