Chapter 6, Problem 3E

1.

To determine

To prepare: Income statement of the company for the year using variable costing.

Explanation of Solution

S. Company Income Statement (Variable Costing) For the year ended December 31, 2017
Particulars	Amount ($)	Amount($)
Sales $\left(70,000\times \$350\right)$		24,500,000
Total Direct Material $\left(70,000\times 40\right)$	(2,800,000)
Total Direct Labor $\left(70,000\times 60\right)$	(4,200,000)
Variable Production Overheads (Working Note)	(2,100,000)
Variable Selling & Administrative Overheads $\left(70,000\times \$30\right)$	(770,000)	(9,870,000)
Contribution Margin		14,630,000
Fixed Production Overheads	(7,000,000)
Fixed Selling & Administrative Overheads	(4,250,000)	(11,250,000)
Net Income		3,380,000
Table (1)

The net income at the year ending Dec 31, 2017 under variable costing is $3,380,000.

Working Note:

The calculation of variable production overhead is,
$\text{Variable Overhead Production Cost}=\text{Number of Units}\times \text{Variable Cost Per Unit}$

Where, number of units can be calculated as,
$\begin{array}{c}\text{Number of Units}=\text{Opening Stock}+\text{Production}-\text{Closing Stock}\\ =0+100,000-30,000\\ =70,000\end{array}$

The calculation of variable cost per unit is,
$\begin{array}{c}\text{Variable Overhead Per Unit}=\frac{\text{Annual Variable Overheads}}{\text{Units Produced}}\\ =\frac{\$3,000,000}{100,000}\\ =\$30\end{array}$

Substitute 70,000 for number of units and $30 for variable overhead per unit in the above formula.
$\begin{array}{c}\text{Variable Overhead Production Cost}=70,000\times \$30\\ =\$2,100,000\end{array}$

Thus, the net income at the year ending Dec 31, 2017 under variable costing is $3,380,000.

2.

To determine

To prepare: Income statement for the year using absorption costing.

Explanation of Solution

S. Company Income Statement (Absorption Costing) For the year ended December 31, 2017
Particulars	Amount($)	Amount($)
Sales $\left(70,000\times \$350\right)$		24,500,000
Cost of Goods Sold (Working Note)		(14,000,000)
Gross Margin		10,500,000
Variable Selling & Administrative Overheads	(770,000)
Fixed Selling & Administrative Overheads	(4,250,000)	(5,020,000)
Net Income		5,480,000
Table (2)

The net income at the year ending Dec 31, 2017 under absorption costing is $5,480,000.

Working note:

Calculation of cost of goods sold is,
$\text{Cost of Goods Sold}=\text{Number of Units Sold}\times \text{Cost Per Unit}$

Where, the cost per unit can be calculated as,

Particulars	Amount ($) Per Unit
Direct Material	40
Direct Labor	60
Variable Overheads	30
Fixed Overheads $\left(\frac{\$7,000,000}{1,00,000}\right)$	70
Total Cost Per Unit	200
Table (3)

Substitute 70,000 for number of units sold and $200 for cost per unit in the above formula.

$\begin{array}{c}\text{Cost of Goods Sold}=70,000\times \$200\\ =14,000,000\end{array}$

Thus, the net income at the year ending Dec 31, 2017 under absorption costing is $5,480,000.

3.

To explain: The circumstances under which the reported income becomes identical under both absorption and variable costing.

• When the closing stock of the firm becomes zero, the reported incomes under both absorption and variable costing become identical.
• The only difference between the variable costing and absorption costing is the valuation of closing or ending inventory, so, whenever the value of ending inventory becomes equal or same, the incomes under both costing methods becomes identical.

Thus, the reported income becomes identical under both absorption and variable method when the values of closing inventory under both the methods become equal.

3.

To determine

To explain: The circumstances under which the reported income becomes identical under both absorption and variable costing.

Explanation of Solution

• When the closing stock of the firm becomes zero, the reported incomes under both absorption and variable costing become identical.
• The only difference between the variable costing and absorption costing is the valuation of closing or ending inventory, so, whenever the value of ending inventory becomes equal or same, the incomes under both costing methods becomes identical.

Thus, the reported income becomes identical under both absorption and variable method when the values of closing inventory under both the methods become equal.