Chapter 18, Problem 5PSA

1.

To determine

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

Explanation of Solution

Product T

Given,
Fixed cost is $125,000.

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,

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

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{cost}\text{per}\text{unit}=\frac{\text{Variable}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$1,600,000}{50,000}\\ =\$32\end{array}$

Calculation of contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution}\text{margin}}{\text{Sales}}\times 100\\ =\frac{\$400,000}{\$2,000,000}\times 100\\ =20\text{\%}\end{array}$

Hence, contribution margin ratio is 20%.

Product O

Given,
Fixed cost is $1,475,000.

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 $1,475,000 for fixed cost and 0.875 for contribution margin ratio.

$\begin{array}{c}\text{Break}-\text{even point}=\frac{\$1,475,000}{0.875}\\ =\$1,685,714.28\end{array}$

Working note:

Calculation of selling price per unit,

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

Calculation of variable cost per unit,

$\begin{array}{c}\text{Variable}\text{cost}\text{per}\text{unit}=\frac{\text{Variable}\text{cost}}{\text{Units}\text{sold}}\\ =\frac{\$250,000}{50,000}\\ =\$5\end{array}$

Formula to calculate contribution margin ratio,

$\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution}\text{margin}}{\text{Sales}}\times 100\\ =\frac{\$1,750,000}{\$2,000,000}\times 100\\ =87.5\text{\%}\end{array}$

Hence, contribution margin ratio is 87.5%.

Hence, break-even point of sale of product T is $625,000 and product O is $1,685,714.28.

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 H
Income Statement
For the Year Ended December 31, 20XX
Particulars	Product T Amount ($)	Product O Amount ($)
Sales	1,200,000	1,200,000
Less: Variable Cost	960,000	150,000
Contribution Margin	240,000	1,050,000
Less: Fixed Cost	125,000	1,475,000
Pre Tax Income	115,000	(425,000)
Tax	36,800	(136,000)
Net Income	78,200	289,000

Table(1)

Working note:

Given,
The numbers of units sold is 30,000.
The selling price is $40 of both products.
Variable cost per unit of product T is $32.
Variable cost per unit of product O is $5.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =30,0\text{00}\text{units}\times \$40\\ =\$1,200,000\end{array}$

The total sales are $1,200,000.

Product T

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =3\text{0,000}\text{units}\times \$32\\ =\$960,000\end{array}$

The total variable cost is $960,000.

Product O

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =3\text{0,000}\text{units}\times \$5\\ =\$150,000\end{array}$

The total variable cost is $150,000.

Product T

Calculation of tax,

` $\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$115,000\times 32\%\\ =\$36,800\end{array}$

Product O

Calculation of tax,

` $\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\left(\$425,000\right)\times 32\%\\ =\left(\$136,000\right)\end{array}$

Hence, the net income of Company H is $78,200 from product T and net loss $136,000 from product O.

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 H
Income Statement
For the Year Ended December 31, 20XX
Particulars	Product T Amount ($)	Product O Amount ($)
Sales	2,400,000	2,400,000
Less: Variable Cost	1,920,000	300,000
Contribution Margin	480,000	2,100,000
Less: Fixed Cost	125,000	1,475,000
Pre Tax Income	355,000	625,000
Tax	113,600	200,000
Net Income	241,400	425,000

Table(2)

Working note:

Given,
The numbers of units sold is 60,000.
The selling price is $40 of both products.
Variable cost per unit of product T is $32.
Variable cost per unit of product O is $5.

Calculation of total sales,

$\begin{array}{c}\text{Total}\text{sales}=\text{Numbers}\text{of}\text{units}\times \text{Sales}\text{price}\\ =60,0\text{00}\text{units}\times \$40\\ =\$2,400,000\end{array}$

The total sales are $2,400,000.

Product T

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =6\text{0,000}\text{units}\times \$32\\ =\$1,920,000\end{array}$

The total variable cost is $1,920,000.

Product O

Calculation of total variable cost,

$\begin{array}{c}\text{Total}\text{variable cost}=\text{Numbers}\text{of}\text{units}\times \text{Variable}\text{cost per unit}\\ =6\text{0,000}\text{units}\times \$5\\ =\$300,000\end{array}$

The total variable cost is $300,000.

Product T

Calculation of tax,

` $\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$355,000\times 32\%\\ =\$113,600\end{array}$

Product O

Calculation of tax,

` $\begin{array}{c}\text{Tax}=\text{Pretax}\text{income}\times \text{Tax}\text{rate}\\ =\$625,000\times 32\%\\ =\$200,000\end{array}$

Hence, the net income of Company H is $241,400 from product T and $425,000 from product O.

4.

To determine

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

Explanation of Solution

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

Hence, product that would greatly experience loss when sales decreases is product O 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.