Question

Smith Company can produce two types of carpet cleaners, Brighter and Cleaner. Data on these two products are as follows:

Sales volume in units Brighter: 400 Cleaner:600 Unit sales price Brighter:$1,000 Cleaner$1,000 Unit variable cost Brighter:200 Cleaner:700 The number of machine hours to produce one unit of Brighter is 1, while the number of machine hours for each unit of Cleaner is 2. Total fixed costs for the manufacture of both products are $307,500.

Required: 1. Determine the breakeven point in total units for Smith Company, assuming that the sales mix (on the basis of relative sales volume in units) remains constant. Use the weighted-average contribution margin approach.

2. At this breakeven level, how many units of each product must be sold? Due to rounding, the total breakeven units for Requirement 2 may differ slightly than in Requirement 1.

3. Using the Indirect approach, what is the overall breakeven point in sales dollars? Use the breakeven units computed in Requirement 1.

Answer 1

Weighted Average Contribution Margin = (Aggreagate sales− Aggregate Variable Expense) ÷ Total Units

WACM = ($1,000,000 − $500,000) ÷ 1,000 = $500,000 ÷ 1,000 = $500 per unit

1. Total Break Even Points (in Units) = Total Fixed Cost ÷ WACM per unit

Break Even Points (in Units) = $307,500 ÷ $500 = 615 Units

2. At BEP, Numbers of unit to be sold of brighter = (615 units × 400) ÷ 1,000 = 246 units

At BEP, Numbers of unit to be sold of Cleaner = (615 units × 600) ÷ 1,000 = 369 units

3. Break Even Point (Sales in Dollars) = Break Even Units × Average Selling Price per unit

Break Even Point (Sales in Dollars) = 615 units × $1,000 = $615,000

Marginal Income Statement
	Brighter-400 units	Cleaner-600 units	Total-1,000
Sales @ $1,000 per unit	$400,000	$600,000	$1,000,000
Less: Variable Cost @ $200 and $700 per unit	($80,000)	($420,000)	($500,000)
Unit Contribution Margin	$320,000	$180,000	$500,000
Machine Hour (MH) required per unit	1	2
Contribution Margin per MH	$800	$150