Chapter 21, Problem 5BP

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 BB:

Given, 50,000 units sold for $800,000, variable costs incurred is $560,000, and fixed costs are $100,000. Contribution margin ratio is 30% (Working note 1).

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

$\begin{array}{c}\text{Break-even point (\$) = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}\\ =\frac{\$100,000}{30\%}\\ =\$333,334\left(\text{Rounded off to next dollar}\right)\end{array}$

Therefore, break-even sales for Product BB for the year are $333,334.

Working note1: Compute the contribution margin ratio

Sales price per unit $\left(\$800,000÷50,000\text{units}\right)$ (A)	$16
Variable costs per unit $\left(\$560,000÷50,000\text{units}\right)$	$11.20
Contribution margin per unit (B)	$4.80
Contribution margin ratio $\left[\left(\text{B}\right)\text{÷}\left(\text{A}\right)\right]\times 100\%$	30%

Table (1)

For Product TT:

Given, 50,000 units sold for $800,000, variable costs incurred is $100,000, and fixed costs are $560,000. Contribution margin ratio is 87.5% (Working note 2).

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

$\begin{array}{c}\text{Break-even point (\$) = }\frac{\text{Fixed costs }}{\text{Contribution margin ratio}}\\ =\frac{\$560,000}{87.5\%}\\ =\$640,000\end{array}$

Working note 2: Compute the contribution margin ratio

Sales price per unit $\left(\$800,000÷50,000\text{units}\right)$ (A)	$16
Variable costs per unit $\left(\$100,000÷50,000\text{units}\right)$	$2
Contribution margin per unit (B)	$14
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 TT for the year are $640,000.

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 33,000 units. Therefore revised sales for Product BB are $528,000$\left(33,000\text{units}\times \text{\$16 per unit}\right)$ and variable costs are $369,600$\left(33,000\text{units}\times \text{\$11}\text{.20 per unit}\right)$ and sales for Product TT are $258,000$\left(33,000\text{units}\times \text{\$16 per unit}\right)$ and variable costs are $66,000$\left(33,000\text{units}\times \text{\$2 per unit}\right)$.

Prepare the contribution margin income statement:

Company S
Forecasted Contribution Margin Income Statement
	Product BB	Product TT
Sales	$528,000	$ 528,000
Less: Variable costs	369,600	66,000
Contribution margin	158,400	462,000
Less: Fixed costs	100,000	560,000
Income before taxes	58,400	(98,000)
Less: Income taxes (32%)	18,688	(31,360)
Net income	$39,712	$(66,640)

Table (2)

Therefore, net income for Product BB is $39,712 and net loss for Production TT are $66,640.

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 64,000 units. Therefore revised sales for Product BB are $1,024,000$\left(64,000\text{units}\times \text{\$16 per unit}\right)$ and variable costs are $716,800$\left(64,000\text{units}\times \text{\$11}\text{.20 per unit}\right)$ and sales for Product TT are $1,024,000$\left(64,000\text{units}\times \text{\$16 per unit}\right)$ and variable costs are $128,000$\left(64,000\text{units}\times \text{\$2 per unit}\right)$.

Prepare the contribution margin income statement:

Company H
Forecasted Contribution Margin Income Statement
	Product BB	Product TT
Sales	$1,024,000	$1,024,000
Less: Variable costs	716,800	128,000
Contribution margin	307,200	896,000
Less: Fixed costs	100,000	560,000
Income before taxes	207,200	336,000
Less: Income taxes (32%)	66,304	107,520
Net income	$140,896	$228,480

Table (3)

Therefore, net income for Product BB is $140,896 and for Production TT is $228,480.

4.

To determine

Identify the Product that would experience a greater increase in income when the sales are increase greatly. Explain the same.

Explanation of Solution

Product TT will experience a greater Increase in the income when the sales are increased greatly. The operating leverage of these two products would yield the same implication.  Precisely, higher operating leverage reveals higher fixed costs, which indicates greater influences on income from changes in sales levels.

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 BB 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 BB are taken on lease with the rent based on asset usage.

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

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