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 Unit sales price Unit variable cost Brighter 400 $1,000 200 Cleaner 600 $1,000 700 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 $287,500. 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

Answer 1

	Brighter	Cleaner	Total
Sales mix ratio	40% [ 400/(400+600) ]	60% [ 600/(400+600) ]
Unit sales price	1000	1000
Unit variable cost	200	700
Unit contribution margin	800	300
(*) Sales mix ratio	40%	60%
Weighted average contribution margin	320	180	500

Required 1:
Break-even point in total units = Total fixed costs / Weighted average contribution margin = 287500 / 500	575	Units

Required 2 :
	Brighter	Cleaner
Break-even point in total units	575	575
Sales mix ratio	40%	60%
Break-even point of each product	230	345

Requirement 3 :
	Brighter	Cleaner	Total
Unit sales price	1000	1000
(*) Sales mix ratio	40%	60%
Weighted average sales price	400	600	1000

Overall break-even point in sales dollars = Break-even point in total units * Weighted average sales price = 575 * 1000

575000