Chapter 18, Problem 6PSA

1.

To determine

To identify: Break- even point of sales in dollars (a) plan 1 and (b) plan 2.

Explanation of Solution

(a)

Plan 1

Given,
Fixed cost is $525,000 $\left(\$200,000+\$325,000\right)$ .

Calculated values,
Contribution margin ratio is 70% or 0.7 (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 $525,000 for fixed cost and 0.7 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$525,000}{0.7}\\ =\$750,000\end{array}$

Working note:

Given,
Material cost is $8.
Labor cost is $5.
Material cost reduced by 50%.
Labor cost reduced by 60%.

Calculation of new material cost,

$\begin{array}{c}\text{Material}\text{cost}=\text{Previous}\text{year}\text{material}\text{cost}\times \left(1-\text{Reduction}\text{in}\text{material}\text{cost}\right)\\ =\$8\times \left(1-0.5\right)\\ =\$8\times 0.5\\ =\$4\end{array}$

Hence, material cost is $4.

Calculation of new labor cost,

$\begin{array}{c}\text{Labor}\text{cost}=\text{Previous}\text{year}\text{labor}\text{cost}\times \left(1-\text{Reduction}\text{in}\text{labor}\text{cost}\right)\\ =\$5\times \left(1-0.6\right)\\ =\$5\times 0.4\\ =\$2\end{array}$

Hence, labor cost is $2.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable}\text{cost}=\left(\begin{array}{l}\text{Materialcost}+\text{Direct}\text{labor}\text{cost}\\ +\text{Variable}\text{overhead}\text{cost}\\ +\text{Variable}\text{selling}\text{and}\text{administrative}\text{costs}\end{array}\right)\\ =\$4+\$2+\$1+\$0.5\\ =\$7.5\end{array}$

Calculation of contribution margin,

$\begin{array}{c}\text{Contribution}\text{margin}=\text{Selling}\text{price}-\text{Variable}\text{cost}\\ =\$25-\$7.50\\ =\$17.50\end{array}$

Compute contribution margin ratio.

Given,
Per unit selling price is $25.

Calculated values,
Unit contribution is $17.50.

Formula to calculate contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Unit}\text{contribution}\text{margin}}{\text{Unit}\text{selling}\text{price}}\\ =\frac{\$17.50}{\$25}\\ =0.7\text{or}70\text{\%}\end{array}$

Hence, contribution margin ratio is 40%.

Plan 2

Given,
Fixed cost is $525,000 $\left(\$200,000+\$325,000\right)$ .

Calculated values,
Contribution margin ratio is 51.67% or 0.5167 (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 $525,000 for fixed cost and 0.5167 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$525,000}{0.5167}\\ =\$1,016,063.48\end{array}$

Working note:

Given,
Selling price is $25.
Selling price increased by 20%.
Volume of sales is 40,000.
Reduction in volume of sales is 10%.

Calculation of new selling price,

$\begin{array}{c}\text{Selling}\text{price}=\text{Previous}\text{year}\text{selling}\text{price}\times \left(1+\text{Increase}\text{in}\text{selling}\text{price}\right)\\ =\$25\times \left(1+0.2\right)\\ =\$25\times 1.2\\ =\$30\end{array}$

Calculation of new sales volume,

$\begin{array}{c}\text{Sales}\text{volume}=\text{Previous}\text{year}\text{sales}\text{volume}\times \left(1-\text{Decrease}\text{in}\text{sales}\text{volume}\right)\\ =40,000\times \left(1-0.1\right)\\ =40,000\times 0.9\\ =36,000\end{array}$

Calculation of contribution margin,

$\begin{array}{c}\text{Contribution}\text{margin}=\text{Selling}\text{price}-\text{Variable}\text{cost}\\ =\$30-\$14.50\\ =\$15.50\end{array}$

Compute contribution margin ratio.

Given,
Per unit selling price is $30.

Calculated values,
Unit contribution is $15.50.

Formula to calculate contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Unit}\text{contribution}\text{margin}}{\text{Unit}\text{selling}\text{price}}\\ =\frac{\$15.50}{\$30}\\ =0.5167\text{or}51.67\text{\%}\end{array}$

Hence, contribution margin ratio is 51.67%.

Hence, break-even point of sale of plan 1 and plan 2 is $750,000 and $ 700,000.

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	Plan 1 ($)	Plan 2 ($)
Sales	1,000,000	1,080,000
Less: Variable Cost	300,000	522,000
Contribution Margin	700,000	558,000
Less: Fixed Cost	525,000	525,000
Pre Tax Income	175,000	33,000
Tax	52,500	9,900
Net Income	122,500	23,100

Table(1)

Working note:

Plan 1

Given,
The numbers of units sold is 40,000.
The selling price is $25.
Variable cost per unit is $17.50.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =40,0\text{00}\text{units}\times \$25\\ =\$1,000,000\end{array}$

The total sales are $1,000,000.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =40,0\text{00}\text{units}\times \$17.50\\ =\$700,000\end{array}$

The total variable cost is $700,000.

Calculation of tax,

$\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$175,000\times 30\%\\ =\$52,500\end{array}$

Plan 2

Given,
The numbers of units sold is 36,000.
The selling price is $30.
Variable cost per unit is $14.50.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =36,0\text{00}\text{units}\times \$30\\ =\$1,080,000\end{array}$

The total sales are $1,080,000.

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =36,0\text{00}\text{units}\times \$14.50\\ =\$522,000\end{array}$

The total variable cost is $522,000.

Calculation of tax,

$\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$33,000\times 30\%\\ =\$9,900\end{array}$

Hence, the net income of Company B through plan 1 and plan 2 is $122,500 and $23,100.