Chapter 3, Problem 66P

Variable-Costing and Absorption-Costing Income

Borques Company produces and sells wooden pallets that are used for moving and stacking materials. The operating costs for the past year were as follows:

During the year, Borques produced 200,000 wooden pallets and sold 204,300 at $9 each. Borques had 8,200 pallets in beginning finished goods inventory; costs have not changed from last year to this year. An actual costing system is used for product costing.

Required:

1. 1. What is the per-unit inventory cost that is acceptable for reporting on Borques’s balance sheet at the end of the year ? How many units are in ending inventory? What is the total cost of ending inventory?
2. 2. Calculate absorption-costing operating income.
3. 3. CONCEPTUAL CONNECTION What would the per-unit inventory cost be under variable costing? Does this differ from the unit cost computed in Requirement 1? Why?
4. 4. Calculate variable-costing operating income.
5. 5. Suppose that Borques Company had sold 196,700 pallets during the year. What would absorption-costing operating income have been? Variable-costing operating income?

To determine

Calculate per unit cost of inventory. Also, calculate the units of ending inventory and total cost of ending inventory.

Explanation of Solution

Cost:

Cost can be defined as the cash and cash equivalent which is incurred against the products or its related services which will benefit the organization in the future. There are two types of costs that are fixed and variable costs.

Calculation of per unit cost of inventory:

Particulars	Amount ($)
Direct material	2.85
Direct labor	1.92
Variable overhead	1.60
Fixed overhead1	0.90
Total	7.27

Table (1)

Therefore, per unit cost of inventory is $7.27.

Use the following formula to calculate the units of ending inventory.

$\text{Units of Ending Inventory}=\left(\begin{array}{c}\text{Opening Finished Goods}+\text{Manufactured Goods}\\ -\text{Closing Finished Goods}\end{array}\right)$

Substitute 8,200 units for opening finished goods, and 200,000 units for manufactured goods and 204,300 units for closing finished goods in the above formula.

$\begin{array}{c}\text{Units of Ending Inventory}=\left(8,20\text{0 units}+200,00\text{0 units}-204,300\text{units}\right)\\ =\text{3,900 units}\end{array}$

Therefore, a unit of ending inventory is 3,900 units.

Use the following formula to calculate the cost of ending inventory.

$\text{Cost of Ending Inventory}=\text{Per-Unit Inventory Cost}\times \text{Units of Ending Inventory}$

Substitute $7.27 for per-unit inventory cost and 3,900 units for units of ending inventory in the above formula.

$\begin{array}{c}\text{Cost of Ending Inventory}=\$7.27\times 3,900\text{units}\\ =\$28,353\end{array}$

Therefore, the cost of ending inventory is $28,353.

Working Note:

1. Calculation of fixed overhead:

$\begin{array}{c}\text{Cost of Fixed Overhead Per unit}=\frac{\text{Fixed Overhead}}{\text{Number of Units Produced}}\\ =\frac{180,000}{200,000}\\ =0.90\end{array}$

To determine

Compute the operating income with the help of absorption costing.

Explanation of Solution

Calculation of operating income:

Particulars	Amount ($)
Sales1	1,838,700
Less: cost of goods sold2	1,485,261
Gross margin	353,439
Less: Selling and administrative expenses	279,870
Operating income	73,569

Table (2)

Working Note:

1. Calculation of sales:

$\begin{array}{c}\text{Sales}=\text{Units Sold}\times \text{Price per unit}\\ \text{=204,300}\times \text{\$9}\\ \text{=\$1,838,700}\end{array}$

2. Calculation of cost of goods sold:

$\begin{array}{c}\text{Cost of Goods Sold}=\text{Units Sold}\times \text{Per Unit Cost of Inventory}\\ =\text{204,300}\times \text{\$7}\text{.27}\\ =\text{\$1,485,261}\end{array}$

To determine

Calculate per unit cost of inventory with the help of variable costing. Also, identify the difference in the amount in part 1.

Explanation of Solution

Calculation of per unit cost of inventory with the help of variable costing:

Particulars	Amount ($)
Direct material	2.85
Direct labor	1.92
Variable overhead	1.60
Total	6.37

Table (3)

Therefore, per unit cost of inventory with the help of variable costing is $6.37.

The difference between per unit cost of inventory occurs because the absorption costing includes the amount of both variable and fixed costing. On the contrary, variable costing does not include the amount of fixed costing. That is why under absorption costing the value of per unit of ending inventory is higher as compared to the variable costing.

To determine

Compute the operating income with the help of variable costing.

Explanation of Solution

Calculation of operating income:

Particulars	Amount ($)
Sales1	1,838,700
Less: cost of goods sold2	1,485,261
Selling and administrative expenses3	183,870
Contribution margin	353,439
Less: Fixed overhead	180,000
Fixed Selling and administrative expenses	96,000
Operating income	77,439

Table (4)

Working Note:

1. Calculation of sales:

$\begin{array}{c}\text{Sales}=\text{Units Sold}\times \text{Price per unit}\\ =\text{204,300}\times \text{\$9}\\ =\text{\$1,838,700}\end{array}$

2. Calculation of cost of goods sold:

$\begin{array}{c}\text{Cost of Goods Sold}=\text{Units Sold}\times \text{Per Unit Cost of Inventory}\\ =\text{204,300}\times \text{\$6}\text{.37}\\ =\text{\$1,301,391}\end{array}$

2. Calculation of selling and administrative expenses:

$\begin{array}{c}\text{Selling and Administrative Expenses}=\text{Units Sold}\times \text{Variable Selling}\\ =\text{204,300}\times \text{\$0}\text{.90}\\ =\text{\$183,870}\end{array}$

To determine

Compute the operating income with the help absorption costing and variable costing:

Explanation of Solution

Calculation of operating income with the help of absorption costing:

Particulars	Amount ($)
Sales1	1,770,300
Less: cost of goods sold2	1,430,009
Gross margin	340,291
Less: Selling and administrative expenses	273,030
Operating income	67,261

Table (5)

Therefore, the amount of operating income under absorption costing is $67,261.

Calculation of operating income with the help of variable costing:

Particulars	Amount ($)
Sales1	1,770,300
Less: cost of goods sold3	1,252,979
Selling and administrative expenses4	177,030
Contribution margin	340,291
Less: Fixed overhead	180,000
Fixed Selling and administrative expenses	96,000
Operating income	64,291

Table (6)

Therefore, the amount of operating income under variable costing is $64,291.

Working Note:

1. Calculation of sales:

$\begin{array}{c}\text{Sales}=\text{Units Sold}\times \text{Price per unit}\\ =\text{196,700}\times \text{\$9}\\ =\text{\$1,770,300}\end{array}$

2. Calculation of cost of goods sold under absorption costing:

$\begin{array}{c}\text{Cost of Goods Sold}=\text{Units Sold}\times \text{Per Unit Cost of Inventory}\\ =\text{196,700}\times \text{\$7}\text{.27}\\ =\text{\$1,430,009}\end{array}$

3. Calculation of cost of goods sold under variable costing:

$\begin{array}{c}\text{Cost of Goods Sold}=\text{Units Sold}\times \text{Per Unit Cost of Inventory}\\ =\text{196,700}\times \text{\$6}\text{.37}\\ =\text{\$1,252,979}\end{array}$

4. Calculation of selling and administrative expenses:

$\begin{array}{c}\text{Selling and Administrative Expenses}=\text{Units Sold}\times \text{Variable Selling}\\ =\text{196,700}\times \text{\$0}\text{.90}\\ =\text{\$177,030}\end{array}$