Chapter 5, Problem 4PSB

1.

To determine

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

Explanation of Solution

Given,
Fixed cost is $200,000.

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 $200,000 for fixed cost and 0.2 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$200,000}{0.2}\\ =\$1,000,000\end{array}$

Working note:

Given,
Sales are $750,000.
Contribution margin is $150,000.

Formula to calculate contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution}\text{margin}}{\text{Sales}}\times 100\\ =\frac{\$150,000}{\$750,000}\times 100\\ =20\text{\%}\end{array}$

Hence, contribution margin ratio is 20%.

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

2.

To determine

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

Explanation of Solution

Given,
Fixed cost is $350,000 $\left(\$200,000+150,000\right)$ .
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 $350,000 for fixed cost and 0.6 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$350,000}{0.6}\\ =\$583333.33\end{array}$

Working note:

Calculation of selling price per unit,

$\begin{array}{c}\text{Selling}\text{price}\text{per}\text{unit}=\frac{\text{Sales}}{\text{Units}\text{sold}}\\ =\frac{\$750,000}{20,000}\\ =\$37.50\end{array}$

Calculation of sales in 2018,

$\begin{array}{c}\text{Sales}=\text{Selling}\text{price}\text{per}\text{units}\times \text{Units}\text{sold}\\ =\$37.50\times 40,000\text{units}\\ =\$1,500,000\end{array}$

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{cost}\text{per}\text{unit}=\frac{\text{Variable}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$600,000}{20,000}\\ =\$30\end{array}$

As new machine reduced variable cost up to 50%, so the new variable cost will be $15.

Calculation of variable cost in 2018,

$\begin{array}{c}\text{Variable}\text{cost}=\text{Variable}\text{cost}\text{per}\text{units}\times \text{Units}\text{sold}\\ =\$15\times 40,000\text{units}\\ =\$600,000\text{units}\end{array}$

Calculation of contribution margin,

$\begin{array}{c}\text{Contribution}\text{margin}=\text{Sales}-\text{Variable}\text{costs}\\ =\$1,500,000-\$600,000\\ =\$900,000\end{array}$

Calculation of contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution}\text{margin}}{\text{Sales}}\times 100\\ =\frac{\$900,000}{\$1,500,000}\times 100\\ =60\text{\%}\end{array}$

Hence, contribution margin ratio is 60%.

Hence, break-even point of sale is $583333.33.

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 R
Income Statement
For the Year Ended 2018
Particulars	Amount ($)
Sales	750,000
Less: Variable Cost	300,000
Contribution Margin	450,000
Less: Fixed Cost	350,000
Pre Tax Income	100,000

Table(1)

Working note:

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

Calculated values (working note),
The selling price is $37.50.
Variable cost per unit is $15.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =20,0\text{00}\text{units}\times \$37.50\\ =\$750,000\end{array}$

The total sales are $750,000.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =20,0\text{00}\text{units}\times \$15\\ =\$300,000\end{array}$

Hence, the pretax income of Company R is $100,000.

4.

To determine

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

Explanation of Solution

Given,
Fixed cost is $350,000.
Target net income is $200,000.

Calculated,
Unit contribution margin is $22.50.

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 $350,000 for fixed cost, $200,000 for target net income and $22.50 for unit contribution margin.

$\begin{array}{c}\text{Required sales}=\frac{\$350,000+\$200,000}{\$22.50}\\ =\frac{\$550,000}{\$22.50}\\ =24,444.44\text{units}\end{array}$

Working note:

Given,
Per unit selling price is $37.50.
Per unit variable cost is $15.

Calculation of unit contribution margin,

$\begin{array}{c}\text{Unit}\text{Contribution}\text{margin}=\text{Per}\text{unit}\text{selling}\text{price}-\text{Per}\text{unit}\text{variable}\text{cost}\\ =\$37.50-\$15\\ =\$22.50\end{array}$

Calculation of required sales in dollars,

$\begin{array}{c}\text{Required sales}=\text{Required sales}\text{in}\text{units}\times \text{Selling}\text{price}\text{per}\text{unit}\\ =24,444\times \$37.50\\ =\$916,666.67\end{array}$

Hence, required sales are 24,444.44 units and $916,666.67.

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 R
Income Statement
For the Year Ended December 31, 2018
Particulars	Amount ($)
Sales	916,667
Less: Variable Cost	366,667
Contribution Margin	550,000
Less: Fixed Cost	350,000
Pre Tax Income	200,000

Table(2)

Working note:

Given,
The numbers of units sold is 24,444.44.

Calculated values (working note),
The selling price is $37.50.
Variable cost per unit is $15.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =24,444.44\text{units}\times \$37.50\\ =916,666.5\end{array}$

The total sales are $916,667.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =24,444.44\text{units}\times \$15\\ =\$366,666.6\end{array}$

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