Chapter 16, Problem 1CE

1. a.

To determine

Compute the variable product cost per unit.

Explanation of Solution

Variable Cost: Variable costs refer to the costs that are involved in the production, and vary as per the changes in the volume of production.

Compute the variable product cost per unit of T-shirt:

$\begin{array}{c}\text{Variable Product Cost}=\text{Direct materials + Direct labor + Variable overhead}\\ =\$5.75+\$1.25+\$0.60\\ =\$7.60\end{array}$

The variable product cost per unit of T-shirt is $7.60.

1. b.

To determine

Compute the total variable cost per unit.

Explanation of Solution

Compute the total variable cost per unit of T-shirt:

$\begin{array}{c}\text{Total Variable Cost}=\left(\begin{array}{l}\text{Direct materials + Direct labor + Variable }\\ \text{overhead + Variable selling expense}\end{array}\right)\\ =\$5.75+\$1.25+\$0.60+\$0.80\\ =\$8.40\end{array}$

The total variable cost per unit of T-shirt is $8.40.

1. c.

To determine

Compute the contribution margin cost per unit.

Explanation of Solution

Contribution Margin: The contribution margin refers to the process or the theory that is used to judge the benefit generated from each unit of the goods produced.

Compute the contribution margin per unit of T-shirt:

$\begin{array}{c}\text{Contribution Margin }=\text{Price}-\text{Variable cost}\\ =\$16.00-\$8.40\\ =\$7.60\end{array}$

The contribution margin per unit of T-shirt is $7.60.

1. d.

To determine

Compute the contribution margin ratio.

Explanation of Solution

Contribution Margin Ratio: The contribution margin ratio shows the amount of difference in the actual sales value and the variable expenses in percentage. This margin indicates that percentage which is available for sale above the fixed costs and the profit. The formula for variable cost ratio is shown below:

$\text{Contribution Margin ratio = }\frac{\text{Contribution Margin}}{\text{Sales}}$

Compute the contribution margin ratio:

$\begin{array}{c}\text{Contribution Margin ratio = }\frac{\text{Contribution Margin}}{\text{Sales}}\\ =\frac{\$7.60}{\$16}\\ =0.475\\ =47.50\%\end{array}$

The contribution margin ratio is 47.50%.

1. e.

To determine

Compute the total fixed expense for the year.

Explanation of Solution

Fixed Cost: Fixed costs refer to the costs which are involved in the production but remain the same and do not change irrespective of the volume of production.

Compute the total fixed expense for the year:

$\begin{array}{c}\text{Fixed expense }=\left(\begin{array}{l}\text{Total fixed factory overhead + Fixed}\\ \text{selling and administrative overhead}\end{array}\right)\\ =\$43,000+\$19,000\\ =\$62,000\end{array}$

The total fixed expense for the year is $62,000.

2.

To determine

Draw up the contribution margin based income statement for Company ST.

Explanation of Solution

Operating income: Operating income refers to the income generated from the operation of

business, or the revenue generated from the services offered by the company.

Compute the operating income for Company ST:

Particulars	Total Amount ($)	Per unit Amount ($)
Sales (1)	$192,000	$16.00
Less: Variable cost (2)	$100,800	$8.40
Contribution margin	$91,200	$7.60
Less: Fixed cost	$62,000
Operating income	$29,200

Table (1)

The operating income for Company ST is $29,200.

Working Note (1):

Compute the value of sales:

$\begin{array}{c}\text{Sales}=\text{Unit Cost }\times \text{ Number of units sold}\\ =\$16\times 12,000\\ =\$192,000\end{array}$

Working Note (2):

Compute the value of variable cost:

$\begin{array}{c}\text{Variable cost}=\text{Variable cost per unit }\times \text{ Number of units sold}\\ =\$8.40\times 12,000\\ =\$100,800\end{array}$

3. a.

To determine

Compute the variable product cost per unit.

Explanation of Solution

Compute the variable product cost per unit of T-shirt:

$\begin{array}{c}\text{Variable Product Cost}=\text{Direct materials + Direct labor + Variable overhead}\\ =\$5.75+\$1.25+\$0.60\\ =\$7.60\end{array}$

The variable product cost per unit of T-shirt is $7.60.

3. b.

To determine

Compute the total variable cost per unit.

Explanation of Solution

Compute the total variable cost per unit of T-shirt:

$\begin{array}{c}\text{Total Variable Cost}=\left(\begin{array}{l}\text{Direct materials + Direct labor + Variable }\\ \text{overhead + Variable selling expense}\end{array}\right)\\ =\$5.75+\$1.25+\$0.60+\$1.75\\ =\$9.35\end{array}$

The total variable cost per unit of T-shirt is $9.35.

3. c.

To determine

Compute the contribution margin cost per unit.

Explanation of Solution

Compute the contribution margin per unit of T-shirt:

$\begin{array}{c}\text{Contribution Margin }=\text{Price}-\text{Variable cost}\\ =\$16.00-\$9.35\\ =\$6.65\end{array}$

The contribution margin per unit of T-shirt is $6.65.

3. d.

To determine

Compute the contribution margin ratio.

Explanation of Solution

Compute the contribution margin ratio:

$\begin{array}{c}\text{Contribution Margin ratio = }\frac{\text{Contribution Margin}}{\text{Sales}}\\ =\frac{\$6.65}{\$16}\\ =0.4156\\ =41.56\%\end{array}$

The contribution margin ratio is 41.56%.

3. e.

To determine

Compute the total fixed expense for the year.

Explanation of Solution

Fixed Cost: Fixed costs refer to the costs which are involved in the production but remain the same and do not change irrespective of the volume of production.

Compute the total fixed expense for the year:

$\begin{array}{c}\text{Fixed expense }=\left(\begin{array}{l}\text{Total fixed factory overhead + Fixed}\\ \text{selling and administrative overhead}\end{array}\right)\\ =\$43,000+\$19,000\\ =\$62,000\end{array}$

The total fixed expense for the year is $62,000.