Chapter 18, Problem 28P

The following information pertains to Vladamir, Inc., for last year:

There are no work-in-process inventories. Normal activity is 100,000 units. Expected and actual overhead costs are the same. Costs have not changed from one year to the next.

Required:

1. 1. How many units are in ending inventory?
2. 2. Without preparing an income statement, indicate what the difference will be between variable-costing income and absorption-costing income.
3. 3. Assume the selling price per unit is $29. Prepare an income statement using (a) variable costing and (b) absorption costing.

To determine

Determine the units of ending inventory.

Explanation of Solution

Determine the units of ending inventory:

Particulars	Units
Beginning inventory	1,320
Add: Units produced	100,000
	101,320
Less: Units sold	(101,000)
Ending inventory	320

Table (1)

Thus, the ending inventory is 320 units.

To determine

Determine the difference between variable costing income and absorption costing income without preparing income statement.

Explanation of Solution

Variable Costing:  The variable costing is the method of costing in which only the variable production costs such as the direct material, direct cost, and variable overhead costs are included in that time period in which they are incurred.

Absorption Costing: Absorption costing is a method for calculating the full cost or total cost of a single product in production process. It includes the total cost assigned to products.

Determine the difference between variable costing income and absorption costing income:

$\begin{array}{c}\begin{array}{l}\text{Difference between absorption }\\ \text{costing income and }\\ \text{variable costing income}\end{array}\}=\left(\begin{array}{l}\text{Absorption costing}\\ \text{ income}\end{array}\right)-\left(\begin{array}{l}\text{Variable costing }\\ \text{income}\end{array}\right)\\ =\text{Fixed overhead rate}\times \left(\text{Production}-\text{Sales}\right)\\ =\$2.34\times \left(100,000\text{ units}-101,000\text{ units}\right)\\ =(\$2,340)\end{array}$

Thus, the difference between variable costing income and absorption costing income is ($2,340).

Working note 1: Calculate the fixed overhead rate:

$\begin{array}{c}\text{Fixed overhead rate}=\frac{\text{Fixed overhead}}{\text{Total number of units}}\\ =\frac{\$234,000}{100,000}\\ =\$2.34\text{ per unit}\end{array}$

To determine

Prepare an income statement using variable costing.

Explanation of Solution

Variable costing income statement: It is one of the important types of income statement, in which the entire variable costs are deducted from the revenue and the company’s contribution margin would be determined. Deducting all the fixed expenses from the contribution margin would result in company’s net income.

Prepare an income statement using variable costing:

Incorporation V
Variable Costing income statement
For last year
Particulars	Amount
Sales $\left(\$29\times 101,000\right)$	$2,929,000
Less: Variable expenses:
Variable cost of goods sold $\left(101,000\times \$18.75\right)$	($1,893,750)
Variable selling expenses $\left(101,000\times \$2\right)$	($202,000)
Contribution margin	$833,250
Less: Fixed expenses:
Fixed overhead	($234,000)
Fixed selling and administrative expenses	($236,000)
Operating income	$363,250

Table (2)

Therefore, the operating income under variable costing is $363,250.

Working note 2: Determine the total cost of goods sold per unit:

$\begin{array}{c}\begin{array}{l}\text{Cost of goods}\\ \text{ sold per unit}\end{array}\}=\left(\begin{array}{l}\text{Direct }\\ \text{materials }\\ \text{per unit}\end{array}\right)+\left(\begin{array}{l}\text{Direct }\\ \text{labor}\\ \text{per unit}\end{array}\right)+\left(\begin{array}{l}\text{Variable}\\ \text{ overhead}\end{array}\right)\\ =\$8.00+\$9.50+\$1.25\\ =\$18.75\end{array}$

To determine

Prepare an income statement using absorption costing.

Explanation of Solution

Absorption costing income statement: It is one of the important types of income statement, in which the cost of goods sold are deducted from the revenue, company’s contribution margin will get. Net income can be calculated by deducting total selling and administrative expenses from the contribution margin of the company.

Prepare and income statement using absorption costing:

Incorporation V
Absorption Costing income statement
For last year
Particulars	Amount
Sales $\left(\$29\times 101,000\right)$	$2,929,000
Less: Cost of goods sold $\left(\$21.09\left(3\right)\times 101,000\right)$	($2,130,090)
Gross profit	$798,910
Less: Selling and administrative expenses (4)	($438,000)
Operating income	$360,910

Table (3)

Hence, the operating income under absorption costing is $360,910.

Working note 3: Determine the total cost of goods sold per unit:

$\begin{array}{c}\begin{array}{l}\text{Cost of goods}\\ \text{ sold per unit}\end{array}\}=\left(\begin{array}{l}\text{Direct }\\ \text{materials }\\ \text{per unit}\end{array}\right)+\left(\begin{array}{l}\text{Direct }\\ \text{labor}\\ \text{per unit}\end{array}\right)+\left(\begin{array}{l}\text{Variable}\\ \text{ overhead}\end{array}\right)+\left(\begin{array}{l}\text{Fixed}\\ \text{ overhead}\end{array}\right)\\ =\$8.00+\$9.50+\$1.25+\$2.34\\ =\$21.09\end{array}$

Working note 4: Determine the total selling and administrative expenses:

$\begin{array}{c}\begin{array}{l}\text{Total selling and }\\ \text{administrative expense}\end{array}\}=\left(\begin{array}{l}\text{Variable selling }\\ \text{expenses}\end{array}\right)+\left(\begin{array}{l}\text{Fixed selling }\\ \text{expenses}\end{array}\right)\\ =\left(\$2\times 101,000\text{ units}\right)+\$236,000\\ =\$202,000+\$236,000\\ =\$438,000\end{array}$