Chapter 18, Problem 46E

1.

To determine

Prepare the income statement under full costing method for the year 2019.

Explanation of Solution

Statement showing the income statement under full costing:

Income statement
For the year 2019
Under full costing method
	2018		2019
Particulars	Amount ($)	Amount ($)	Amount ($)	Amount ($)
Sales (1)		6,704,000		5,586,000
Less: Cost of goods sold
Beginning inventory (2)	1,100,000		1,925,000
Cost of good produced (3)	5,225,000		3,162,500
Cost of good available for sales	6,325,000		5,087,500
Less: Ending inventory (4)	1,925,000		1,237,500
Cost of goods sold	4,400,000		3,850,000
Plus: Production volume variance (5)	35,000		192,500
Adjusted cost of goods sold		4,435,000		4,042,500
Gross margin		2,269,000		1,543,500
Less: Selling and administrative
Variable (6)	400,000		350,000
Fixed	120,000	520,000	120,000	470,000
Operating income		1,749,000		1,073,500

Table (1)

Therefore, the operating income is 1,073,500.

Working notes:

1) Calculate the sales:

For the year 2018:

$\begin{array}{c}\text{Sales}=\left(\text{Units}\times \text{Selling price per unit}\right)\\ =\left(3200\times \$2095\right)\\ =\$6,704,000\end{array}$

For the year 2019:

$\begin{array}{c}\text{Sales}=\left(\text{Units}\times \text{Selling price per unit}\right)\\ =\left(2800\times \$1995\right)\\ =\$5,586,000\end{array}$

2) Calculate the beginning inventory:

For the year 2018:

$\begin{array}{c}\text{Beginning inventory}=\left(\text{Beginning units}\times \text{Total manufacturing cost}\right)\\ =\left(800\times \$1,375\right)\\ =\$1,100,000\end{array}$

For the year 2019:

$\begin{array}{c}\text{Beginning inventory}=\left(\text{Beginning units}\times \text{Total manufacturing cost}\right)\\ =\left(1,400\times \$1,375\right)\\ =\$1,925,000\end{array}$

3) Calculate the cost of goods produced:

For the year 2018:

$\begin{array}{c}\text{Cost of goods produced}=\left(\text{Actual production}\times \text{Total manufacturing cost}\right)\\ =\left(3,800\times \$1,375\right)\\ =\$5,225,000\end{array}$

For the year 2019:

$\begin{array}{c}\text{Cost of goods produced}=\left(\text{Actual production}\times \text{Total manufacturing cost}\right)\\ =\left(2,300\times \$1,375\right)\\ =\$3,162,500\end{array}$

4) Calculate the ending inventory:

For the year 2018:

$\begin{array}{c}\text{Ending inventory}=\left(\text{Ending units}\times \text{Total manufacturing cost}\right)\\ =\left(1,400\times \$1,375\right)\\ =\$19,25,000\end{array}$

For the year 2019:

$\begin{array}{c}\text{Ending inventory}=\left(\text{Ending units}\times \text{Total manufacturing cost}\right)\\ =\left(900\times \$1,375\right)\\ =\$12,37,500\end{array}$

5) Calculate the production volume variance:

For the year 2018:

$\begin{array}{c}\left(\begin{array}{l}\text{Production volume }\\ \text{variance}\end{array}\right)=\left(\text{Difference in production}\times \text{Fixed mnaufacturing cost}\right)\\ =\left(200\times \$175\right)\\ =\$35,000\end{array}$

For the year 2019:

$\begin{array}{c}\left(\begin{array}{l}\text{Production volume }\\ \text{variance}\end{array}\right)=\left(\text{Difference in production}\times \text{Fixed mnaufacturing cost}\right)\\ =\left(1,100\times \$175\right)\\ =\$192,500\end{array}$

6) Calculate the variable cost:

For the year 2018:

$\begin{array}{c}\left\{\begin{array}{l}\text{Selling and administrative }\\ \text{variable cost}\end{array}\right\}=\left(\left(\begin{array}{l}\text{Selling and administrative}\\ \text{ cost per unit}\end{array}\right)\times \text{Units sold}\right)\\ =\left(\$125\times 3,200\right)\\ =\$400,000\end{array}$

For the year 2019:

$\begin{array}{c}\left\{\begin{array}{l}\text{Selling and administrative }\\ \text{variable cost}\end{array}\right\}=\left(\left(\begin{array}{l}\text{Selling and administrative}\\ \text{ cost per unit}\end{array}\right)\times \text{Units sold}\right)\\ =\left(\$125\times 2,800\right)\\ =\$350,000\end{array}$

2.

To determine

Prepare income statement under variable costing for each period.

Explanation of Solution

Prepare income statement under variable costing.

Particulars	2018		2019
	Amount ($)	Amount ($)	Amount ($)	Amount ($)
Sales		6,704,000 (1)		5,586,000 (1)
Less: Cost of goods sold
Beginning inventory (7)	960,000		1,680,000
Cost of good produced (8)	4,560,000		2,760,000
Cost of good available for sales	5,520,000		4,440,000
Less: Ending inventory (9)	1,680,000		1,080,000
Cost of goods sold	3,840,000		3,360,000
Plus: Variable selling and administrative (6)	400,000	4,240,000	350,000	3,710,000
Contribution margin		2,464,000		1,876,000
Less: Fixed manufacturing cost		700,000		595,000
Less: Fixed Selling and administrative		120,000		120,000
Operating income		1,644,000		1,161,000

Table (2)

Therefore, the operating income is $1,644,000 for the year 2018 and $1,161,000 for the year 2019.

Calculate the difference in operating income:

Particular	2018	2019
Change in inventory (a)	600	(500)
Fixed overhead rate (b)	$175	$175
Difference in net income (a x b)	$105,000	($87,500)

Table (3)

An increase in inventory units shows the operating income under full costing method to be higher than the operating income under variable costing method and vice versa.

During the year 2018, the level of inventory units increased hence the operating income under full costing is higher than variable costing method.

During the year 2019, the level of inventory unit decreased hence the operating income under full costing method is lower than variable costing method.

Working notes:

7) Calculate the beginning inventory:

For the year 2018:

$\begin{array}{c}\text{Beginning inventory}=\left(\text{Beginning units}\times \text{Manufacturing variable cost}\right)\\ =\left(800\times \$1,200\right)\\ =\$960,000\end{array}$

For the year 2019:

$\begin{array}{c}\text{Beginning inventory}=\left(\text{Beginning units}\times \text{Manufacturing variable cost}\right)\\ =\left(1400\times \$1,200\right)\\ =\$1,680,000\end{array}$

8) Calculate the cost of goods produced:

For the year 2018:

$\begin{array}{c}\text{Cost of goods produced}=\left(\text{Actual production}\times \text{Total manufacturing cost}\right)\\ =\left(3800\times \$1,200\right)\\ =\$4,560,000\end{array}$

For the year 2019:

$\begin{array}{c}\text{Cost of goods produced}=\left(\text{Actual production}\times \text{Total manufacturing cost}\right)\\ =\left(2,300\times \$1,200\right)\\ =\$2,760,000\end{array}$

9) Calculate the ending inventory:

For the year 2018:

$\begin{array}{c}\text{Ending inventory}=\left(\text{Ending units}\times \text{Total manufacturing cost}\right)\\ =\left(1400\times \$1,200\right)\\ =\$1,680,000\end{array}$

For the year 2019:

$\begin{array}{c}\text{Ending inventory}=\left(\text{Ending units}\times \text{Total manufacturing cost}\right)\\ =\left(900\times \$1,200\right)\\ =\$1,080,000\end{array}$

3.

To determine

Explain the changes in operating income between variable costing and full costing in a brief memo.

Explanation of Solution

The following is the changes in the operating income between variable costing and full costing:

MEMO

To: Mr. M

From:

Date:

The change in operating income is due to the change in finished inventory that is during the year 2018, the inventory increased by 600 units and during the year 2019, the inventory decreased by 500 units. The income statement under variable costing does not include fixed manufacturing cost but treated as current period cost. So the income statement under variable costing is not affected due to this change.

In case of income statement under full costing, it includes the fixed cost in inventory. Due to this the operating income shows a lesser amount in the period in which there is change in level of inventory. The reason for the decrease is that the fixed cost is included in the cost of goods sold during these periods.