Chapter 18, Problem 5PSB

1.

To determine

To identify: Break- even point of sales in dollars for each product.

Explanation of Solution

Product BB

Given,
Fixed cost is $100,000.

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 $125,000 for fixed cost and 0.2 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$125,000}{0.2}\\ =\$625,000\end{array}$

Working note:

Calculation of selling price per unit,

$\begin{array}{c}\text{Selling}\text{price}\text{per}\text{unit}=\frac{\text{Sales}}{\text{Units}\text{sold}}\\ =\frac{\$800,000}{50,000}\\ =\$16\end{array}$

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{cost}\text{per}\text{unit}=\frac{\text{Variable}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$560,000}{50,000}\\ =\$11.20\end{array}$

Calculation of contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution}\text{margin}}{\text{Sales}}\times 100\\ =\frac{\$240,000}{\$800,000}\times 100\\ =30\text{\%}\end{array}$

Hence, contribution margin ratio is 30%.

Product TT

Given,
Fixed cost is $560,000.

Calculated values,
Contribution margin ratio is 87.5% or 0.875 (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 $560,000 for fixed cost and 0.875 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$560,000}{0.875}\\ =\$640,000\end{array}$

Working note:

Calculation of selling price per unit,

$\begin{array}{c}\text{Selling}\text{price}\text{per}\text{unit}=\frac{\text{Sales}}{\text{Units}\text{sold}}\\ =\frac{\$800,000}{50,000}\\ =\$16\end{array}$

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{cost}\text{per}\text{unit}=\frac{\text{Variable}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$100,000}{50,000}\\ =\$2\end{array}$

Calculation of contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution}\text{margin}}{\text{Sales}}\times 100\\ =\frac{\$700,000}{\$800,000}\times 100\\ =87.5\text{\%}\end{array}$

Hence, contribution margin ratio is 87.5%.

Hence, break-even point of sale of Product BB is $625,000 and Product TT is $640,000.

2.

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 S
Income Statement
For the Year Ended December 31, 20XX
Particulars	Product BB Amount ($)	Product TT Amount ($)
Sales	528,000	528,000
Less: Variable Cost	369,600	66,000
Contribution Margin	158,400	462,000
Less: Fixed Cost	100,000	560,000
Pre Tax Income	58,400	(98,000)
Tax	18,688	(31,360)
Net Income	39,712	(66,640)

Table(1)

Working note:

Given,
The numbers of units sold is 33,000.
The selling price is $16 of both products.
Variable cost per unit of Product BB is $11.20.
Variable cost per unit of Product TT is $2.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =33,0\text{00}\text{units}\times \$16\\ =\$528,000\end{array}$

The total sales are $528,000.

Product BB

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =33\text{,000}\text{units}\times \$11.20\\ =\$369,600\end{array}$

The total variable cost is $369,600.

Product TT

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =33\text{,000}\text{units}\times \$2\\ =\$66,000\end{array}$

The total variable cost is $66,000.

Product BB

Calculation of tax,

` $\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$584,000\times 32\%\\ =\$186,880\end{array}$

Product TT

Calculation of tax,

` $\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\left(\$98,000\right)\times 32\%\\ =\left(\$31,360\right)\end{array}$

Hence, the net income of Company S is $39,712 from Product BB and net loss $66,640 from Product TT.

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 S
Income Statement
For the Year Ended December 31, 20XX
Particulars	Product BB Amount ($)	Product TT Amount ($)
Sales	1,024,000	1,024,000
Less: Variable Cost	716,800	128,000
Contribution Margin	307,200	896,000
Less: Fixed Cost	100,000	560,000
Pre Tax Income	207,200	336,000
Tax	66,304	107,520
Net Income	140,896	228,480

Table(2)

Working note:

Given,
The numbers of units sold is 64,000.
The selling price is $16 of both products.
Variable cost per unit of Product BB is $11.20.
Variable cost per unit of Product TT is $2.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =64,0\text{00}\text{units}\times \$16\\ =\$1,024,000\end{array}$

The total sales are $1,024,000.

Product BB

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =64\text{,000}\text{units}\times \$11.20\\ =\$716,800\end{array}$

The total variable cost is $716,800.

Product TT

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =64\text{,000}\text{units}\times \$2\\ =\$128,000\end{array}$

The total variable cost is $128,000.

Product BB

Calculation of tax,

` $\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$207,200\times 32\%\\ =\$66,304\end{array}$

Product TT

Calculation of tax,

` $\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$33,600\times 32\%\\ =\$10,752\end{array}$

Hence, the net income of Company S is $140,896 from Product BB and $228,480 from Product TT.

4.

To determine

To identify: The product that would greatly experience loss when sales decreases.

Explanation of Solution

• The Product TT will experience greater loss when sales decreases.
• Per unit variable cost is low of Product TT therefore, contribution is highly affected due to decrease in sales.
• Fixed cost is high of product TT therefore; when sales highly decrease the product TT have to suffer huge losses.

Hence, product that would greatly experience loss when sales decreases is product TT as its fixed expenses are higher.

5.

To determine

To identify: The factors that might have created the different cost structure for the two products.

Explanation of Solution

The factors that might have created the different cost structure for the two products:

• Labor cost: It may affect the cost structure as it is one of the important parts of total cost it includes the wages paid to the workers.
• Machinery cost: It may affect the cost structure as it is one of the important parts of total cost it includes the cost incurred to install machinery.
• Salary of staff: It may affect the cost structure as it is one of the important parts of total cost it depends on the number of staff working in the organization.
• Raw material cost: It may affect the cost structure as it is one of the important parts of total cost, raw material required may be more or less costly therefore, it also affect a product’s cost.

Hence, raw material cost, salary structure, machinery required etc are the factors that might have created the different cost structure for the two products.