Chapter 21, Problem 5AP

1.

To determine

Compute the break-even point in dollar sales for each product.

Explanation of Solution

Break-Even Point: It is the point of sales at which entity neither earns a profit nor suffers a loss. It can also be said that the point of sales at which sales value of the entity recovers the entire cost of fixed and variable nature is called break-even point

$\text{Break-even point (\$) = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}$

For product T:

Given, 50,000 units sold for $2,000,000, variable costs incurred is $1,600,000, and fixed costs are $125,000. Contribution margin ratio is 20% (Working note 1).

Compute the break-even point in dollar sales for year:

$\begin{array}{c}\text{Break-even point (\$) = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}\\ =\frac{\$125,000}{20\%}\\ =\$625,000\end{array}$

Therefore, break-even sales for Product T for the year are $625,000.

Working note1: Compute the contribution margin ratio

Sales price per unit $\left(\$2,000,000÷50,000\text{units}\right)$ (A)	$40
Variable costs per unit $\left(\$1,600,000÷50,000\text{units}\right)$	$32
Contribution margin per unit (B)	$8
Contribution margin ratio $\left[\left(\text{B}\right)\text{÷}\left(\text{A}\right)\right]\times 100\%$	20%

Table (1)

For product O:

Given, 50,000 units sold for $2,000,000, variable costs incurred is $250,000, and fixed costs are $1,475,000. Contribution margin ratio is 87.5% (Working note 2).

Compute the break-even point in dollar sales for year:

$\begin{array}{c}\text{Break-even point (\$) = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}\\ =\frac{\$1,475,000}{87.5\%}\\ =\$1,685,714\end{array}$

Working note 2: Compute the contribution margin ratio

Sales price per unit $\left(\$2,000,000÷50,000\text{units}\right)$ (A)	$50
Variable costs per unit $\left(\$250,000÷50,000\text{units}\right)$	$5
Contribution margin per unit (B)	$45
Contribution margin ratio $\left[\left(\text{B}\right)\text{÷}\left(\text{A}\right)\right]\times 100\%$	87.5%

Table (1)

Therefore, break-even sales for Product O for the year are $1,685,714.

2.

To determine

Prepare the contribution margin income statement.

Explanation of Solution

Contribution margin income statement: It is a kind of income statement which reports the sales, variable costs, contribution margin, fixed costs, and net profit.

Sales are declined to 30,000 units. Therefore revised sales for product T are $1,200,000$\left(30,000\text{units}\times \text{\$40 per unit}\right)$ and variable costs are $960,000$\left(30,000\text{units}\times \text{\$32 per unit}\right)$ and sales for Product O are $1,200,000$\left(30,000\text{units}\times \text{\$40 per unit}\right)$ and variable costs are $150,000$\left(30,000\text{units}\times \text{\$5 per unit}\right)$.

Prepare the contribution margin income statement:

Company H
Forecasted Contribution Margin Income Statement
	Product T	Product O
Sales	$1,200,000	$1,200,000
Less: Variable costs	960,000	150,000
Contribution margin	240,000	1,050,000
Less: Fixed costs	125,000	1,475,000
Income before taxes	115,000	(425,000)
Less: Income taxes (32%)	36,800	(136,000)
Net income	$78,200	$(289,000)

Table (2)

Therefore, net income for Product T is $78,200 and net loss for Production O are $289,000.

3.

To determine

Prepare the contribution margin income statement.

Explanation of Solution

Contribution margin income statement: It is a kind of income statement which reports the sales, variable costs, contribution margin, fixed costs, and net profit.

Sales are increased to 60,000 units. Therefore revised sales for product T are $2,400,000$\left(60,000\text{units}\times \text{\$40 per unit}\right)$ and variable costs are $1,920,000$\left(60,000\text{units}\times \text{\$32 per unit}\right)$ and sales for Product O are $2,400,000$\left(60,000\text{units}\times \text{\$40 per unit}\right)$ and variable costs are $300,000$\left(60,000\text{units}\times \text{\$5 per unit}\right)$.

Prepare the contribution margin income statement:

Company H
Forecasted Contribution Margin Income Statement
	Product T	Product O
Sales	$2,400,000	$2,400,000
Less: Variable costs	1,920,000	300,000
Contribution margin	480,000	2,100,000
Less: Fixed costs	125,000	1,475,000
Income before taxes	355,000	625,000
Less: Income taxes (32%)	113,600	200,000
Net income	$241,000	$425,000

Table (3)

Therefore, net income for Product T is $241,000 and for Production O is $425,000.

4.

To determine

Identify the product that would experience a greater loss when the sales are decreases greatly. Explain the same.

Explanation of Solution

Product O will experience a greater loss when the sales are decreased greatly. When the sales decreased to zero sales then Product O’s loss is equal to its fixed cost amount ($1,475,000), where Product T’s loss will be equal to $125,000.

5.

To determine

Describe some factors that might have created the different cost structures for these two products.

Explanation of Solution

Factors that could cause Product T to have lower fixed costs might include:

• The labours are paid based on the units produced.
• Sales representatives work only on the basis sales commission.
• Managers are remunerated with a share of profits instead of salaries.
• Assets that are used in production of Product T are taken on lease with the rent based on asset usage.

In contrast, fixed costs for Product O may be higher because of:

• A salary structure that is not based on production or sales.
• Product O's assets that are owned or obtained under a lease agreement based on time, and not on asset usage.