Chapter 5, Problem 6PSB

1.

To determine

To identify: Break- even point of sales in dollars (a) existing business strategy and (b) new business strategy.

Explanation of Solution

(a)

Existing business strategy

Given,
Fixed cost is $950,000.

Calculated values,
Contribution margin ratio is 55% or 0.55 (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 $950,000 for fixed cost and 0.55 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$950,000}{0.55}\\ =\$1,727,272.72\end{array}$

Working note:

Given,
Total variable unit cost is $800,000.
Total variable packaging cost is $100,000.
Units sold are 100,000.
Selling price per unit is $20.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable}\text{cost}=\text{Total variable unit cost}+\text{Total variable packaging cost}\\ =\$800,000+\$100,000\\ =\$900,000\end{array}$

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{cost}\text{per}\text{unit}=\frac{\text{Total}\text{Variable}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$900,000}{100,000}\\ =\$9\end{array}$

Calculation of contribution margin,

$\begin{array}{c}\text{Contribution}\text{margin}=\text{Selling}\text{price}-\text{Variable}\text{cost}\\ =\$20-\$9\\ =\$11\end{array}$

Compute contribution margin ratio.

Given,
Per unit selling price is $20.

Calculated values,
Unit contribution is $11.

Formula to calculate contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Unit}\text{contribution}\text{margin}}{\text{Unit}\text{selling}\text{price}}\\ =\frac{\$11}{\$20}\\ =0.55\text{or}55\text{\%}\end{array}$

Hence, contribution margin ratio is 55%.

New business strategy

Given,
Fixed cost is $950,000.

Calculated values,
Contribution margin ratio is 55% or 0.55 (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 $950,000 for fixed cost and 0.55 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$950,000}{0.55}\\ =\$1,727,273\end{array}$

Working note:

Given,
Selling price is $20.
Selling price decreased by 20%.
Volume of sales is 100,000.
Volume of sales increase by 80%.
Variable cost of packaging increases by 20%.
Variable cost of packaging is $100,000.

Calculation of decreased selling price,

$\begin{array}{c}\text{Selling}\text{price}=\text{Previous}\text{year}\text{selling}\text{price}\times \left(1-\text{Decrease}\text{in}\text{selling}\text{price}\right)\\ =\$20\times \left(1-0.2\right)\\ =\$20\times 0.8\\ =\$16\end{array}$

Calculation of increased sales volume,

$\begin{array}{c}\text{Sales}\text{volume}=\text{Previous}\text{year}\text{sales}\text{volume}\times \left(1+\text{Increase}\text{in}\text{sales}\text{volume}\right)\\ =100,000\times \left(1+0.8\right)\\ =100,000\times 1.8\\ =180,000\end{array}$

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{packaging}\text{cost}\text{per}\text{unit}=\frac{\text{Total}\text{variable}\text{packaging}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$100,000}{100,000}\\ =\$1\end{array}$

Calculation of increased variable packaging cost per unit,

$\begin{array}{c}\text{New}\text{variable}\text{packaging cost}=\left(\begin{array}{l}\text{Previous}\text{year}\text{variable}\text{cost}\\ \times \left(1+\text{Increase}\text{in}\text{variable}\text{cost}\right)\end{array}\right)\\ =\$1\times \left(1+0.2\right)\\ =\$1\times 1.2\\ =\$1.2\end{array}$

Calculation of increased total variable packaging cost,

$\begin{array}{c}\text{Total}\text{variable}\text{packaging cost}=\text{Incresed}\text{variable}\text{cost}\text{per}\text{unit}\times \text{Units}\text{sold}\\ =\$1.2\times 180,000\\ =\$216,000\end{array}$

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{unit}\text{cost}=\frac{\text{Total}\text{variable}\text{unit}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$800,000}{100,000}\\ =\$8\end{array}$

Calculation of decreased variable unit cost per unit,

$\begin{array}{c}\text{New}\text{variable}\text{unit cost}=\left(\begin{array}{l}\text{Previous}\text{year}\text{variable}\text{cost}\\ \times \left(1-\text{Decrease}\text{in}\text{variable}\text{unit}\text{cost}\right)\end{array}\right)\\ =\$8\times \left(1-0.25\right)\\ =\$8\times 0.75\\ =\$6\end{array}$

Calculation of total variable unit cost,

$\begin{array}{c}\text{Total}\text{variable}\text{packaging cost}=\text{Variable}\text{unit}\text{cost}\text{per}\text{unit}\times \text{Units}\text{sold}\\ =\$6\times 180,000\\ =\$1,080,000\end{array}$

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable}\text{cost}=\left(\begin{array}{l}\text{Total}\text{variable}\text{unit}\text{cost}\\ +\text{Total}\text{variable}\text{packaging cost}\end{array}\right)\\ =\$1,080,000+\$216,000\\ =\$1,296,000\end{array}$

Total variable cost per unit is $7.20 $\left(\$1.2+\$6\right)$ .

Calculation of contribution margin,

$\begin{array}{c}\text{Contribution}\text{margin}=\text{Selling}\text{price}-\text{Variable}\text{cost}\\ =\$16-\$7.20\\ =\$8.80\end{array}$

Compute contribution margin ratio.

Given,
Per unit selling price is $16.

Calculated values,
Unit contribution is $8.80.

Formula to calculate contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Unit}\text{contribution}\text{margin}}{\text{Unit}\text{selling}\text{price}}\\ =\frac{\$8.80}{\$16}\\ =0.55\text{or}55\%\end{array}$

Hence, contribution margin ratio is 55%.

Hence, break-even point of sale of existing business strategy and new business strategy is $1,727,273 and $ 1,727,273.

2.

To determine

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

Explanation of Solution

Statement to show the contribution margin income statement

Company B
Income Statement
For the Year Ended December….
Particulars	Existing business strategy ($)	New business strategy ($)
Sales	2,000,000	2,880,000
Less: Variable Cost	900,000	1,296,000
Contribution Margin	1,100,000	1,584,000
Less: Fixed Cost	950,000	950,000
Pre Tax Income	150,000	634,000
Tax	37,500	158,500
Net Income	112,500	475,500

Table(1)

Working note:

Existing business strategy

Given,
The numbers of units sold is 100,000.
The selling price is $20.
Variable cost per unit is $9.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =100,0\text{00}\text{units}\times \$20\\ =\$2,000,000\end{array}$

The total sales are $2,000,000.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =100,0\text{00}\text{units}\times \$9\\ =\$900,000\end{array}$

The total variable cost is $900,000.

Calculation of tax,

$\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$150,000\times 25\%\\ =\$37,500\end{array}$

New business strategy

Given,
The numbers of units sold is 180,000.
The selling price is $16.
Variable cost per unit is $7.20.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =180,0\text{00}\text{units}\times \$16\\ =\$2,880,000\end{array}$

The total sales are $2,880,000.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =180,0\text{00}\text{units}\times \$7.20\\ =\$1,296,000\end{array}$

The total variable cost is $1,296,000.

Calculation of tax,

$\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$634,000\times 25\%\\ =\$158,500\end{array}$

Hence, the net income of Company B through existing business strategy and new business strategy is $112,500 and $475,500.