Chapter 18, Problem 4PSA

1.

To determine

To identify: Break- even point of sales in dollars for year 2017.

Explanation of Solution

Given,
Fixed cost is $250,000.

Calculated values,
Contribution margin ratio is 20% or 0.2 (from working note).

Formula to calculate break-even point of sales in dollars,

$\text{Break}-\text{even point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution margin ratio}}$

Substitute $250,000 for fixed cost and 0.2 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$250,000}{0.2}\\ =\$1,250,000\end{array}$

Working note:

Given,
Sales are $1,000,000.
Contribution margin is $200,000.

Formula to calculate contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution}\text{margin}}{\text{Sales}}\times 100\\ =\frac{\$200,000}{\$1,000,000}\times 100\\ =20\text{\%}\end{array}$

Hence, contribution margin ratio is 20%.

Hence, break-even point of sale is $1,250,000.

2.

To determine

To identify: Break- even point of sales in dollars for year 2018.

Explanation of Solution

Given,
Fixed cost is $450,000 $\left(\$250,000+200,000\right)$ .
Units sold are 40,000 units.

Calculated values,
Contribution margin ratio is 60% or 0.6 (from working note).

Formula to calculate break-even point of sales in dollars,

$\text{Break}-\text{even point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution margin ratio}}$

Substitute $450,000 for fixed cost and 0.6 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$450,000}{0.6}\\ =\$750,000\end{array}$

Working note:

Calculation of selling price per unit,

$\begin{array}{c}\text{Selling}\text{price}\text{per}\text{unit}=\frac{\text{Sales}}{\text{Units}\text{sold}}\\ =\frac{\$1,000,000}{20,000}\\ =\$50\end{array}$

Calculation of sales in 2018,

$\begin{array}{c}\text{Sales}=\text{Selling}\text{price}\text{per}\text{units}\times \text{Units}\text{sold}\\ =\$50\times 40,000\text{units}\\ =\$2,000,000\end{array}$

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{cost}\text{per}\text{unit}=\frac{\text{Variable}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$800,000}{20,000}\\ =\$40\end{array}$

As new machine reduced variable cost up to 50%, so the new variable cost will be $20.

Calculation of variable cost in 2018,

$\begin{array}{c}\text{Variable}\text{cost}=\text{Variable}\text{cost}\text{per}\text{units}\times \text{Units}\text{sold}\\ =\$20\times 40,000\text{units}\\ =\$800,000\text{units}\end{array}$

Calculation of contribution margin,

$\begin{array}{c}\text{Contribution}\text{margin}=\text{Sales}-\text{Variable}\text{costs}\\ =\$2,000,000-\$800,000\\ =\$1,200,000\end{array}$

Formula to calculate contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution}\text{margin}}{\text{Sales}}\times 100\\ =\frac{\$1,200,000}{\$2,000,000}\times 100\\ =60\text{\%}\end{array}$

Hence, contribution margin ratio is 60%.

Hence, break-even point of sale is $750,000.

3.

To determine

To prepare: A forecasted contribution margin income statement for the company.

Explanation of Solution

Statement to show the contribution margin income statement

Company A
Income Statement
For the Year Ended December 31, 2018
Particulars	Amount ($)
Sales	1,000,000
Less: Variable Cost	400,000
Contribution Margin	600,000
Less: Fixed Cost	450,000
Pre Tax Income	150,000

Table(1)

Working note:

Given,
The numbers of units sold is 20,000.

Calculated values (working note),
The selling price is $50.
Variable cost per unit is $40.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =20,0\text{00}\text{units}\times \$50\\ =\$1,000,000\end{array}$

The total sales are $1,000,000.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =20,0\text{00}\text{units}\times \$40\\ =\$800,000\end{array}$

The total variable cost is $800,000. As new machine reduced variable cost up to 50%, so the new variable cost will be $400,000.

Hence, the pretax income of Company A is $150,000.

4.

To determine

To identify: The required sales unit to earn the target income.

Explanation of Solution

Given,
Fixed cost is $450,000.
Target net income is $200,000.

Calculated,
Unit contribution margin is $30.

Formula to calculate required sales will be,

$\text{Required sales}=\frac{\text{Fixed cost}+\text{Target net income}}{\text{Unit}\text{contribution}\text{margin}}$

Substitute $450,000 for fixed cost, $200,000 for target net income and $30 for unit contribution margin.

$\begin{array}{c}\text{Required sales}=\frac{\$450,000+\$200,000}{\$30}\\ =\frac{\$650,000}{\$30}\\ =21,666.67\text{units}\end{array}$

Working note:

Given,
Per unit selling price is $50.
Per unit variable cost is $20.

Calculation of unit contribution margin,

$\begin{array}{c}\text{Unit}\text{Contribution}\text{margin}=\text{Per}\text{unit}\text{selling}\text{price}-\text{Per}\text{unit}\text{variable}\text{cost}\\ =\$50-\$20\\ =\$30\end{array}$

Calculation of required sales in dollars,

$\begin{array}{c}\text{Required sales}=\text{Required sales}\text{in}\text{units}\times \text{Selling}\text{price}\text{per}\text{unit}\\ =21,667\times \$50\\ =\$1,083,350\end{array}$

Hence, required sales are 21,667 units and $1,083,350.

5.

To determine

To prepare: A forecasted contribution margin income statement for the company when no income tax is due.

Explanation of Solution

Statement to show the contribution margin income statement

Company A
Income Statement
For the Year Ended December 31, 2018
Particulars	Amount ($)
Sales	1,083,333
Less: Variable Cost	433,333
Contribution Margin	650,000
Less: Fixed Cost	450,000
Pre Tax Income	200,000

Table(2)

Working note:

Given,
The numbers of units sold is 21,666.67.

Calculated values (working note),
The selling price is $50.
Variable cost per unit is $20.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =21,666.67\text{units}\times \$50\\ =\$1,083,333.5\end{array}$

The total sales are $1,083,333.5.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =21,666.67\text{units}\times \$20\\ =\$433,333.4\end{array}$

Hence, the pretax income of Company A is $200,000.