Question

Suppose that Head-First Company now sells both bicycle helmets and motorcycle helmets. The bicycle helmets are priced at $77 and have variable costs of $47 each. The motorcycle helmets are priced at $220 and have variable costs of $145 each. Total fixed cost for Head-First as a whole equals $57,000 (includes all fixed factory overhead and fixed selling and administrative expense). Next year, Head-First expects to sell 4,850 bicycle helmets and 1,940 motorcycle helmets.

	Required:
1.	Form a package of bicycle and motorcycle helmets based on the sales mix expected for the coming year.
2.	Calculate the break-even point in units for bicycle helmets and for motorcycle helmets.
3.	Check your answer by preparing a contribution margin income statement.

Answer 1

1) Sales mix

	Bicycle helmets	Motorcycle helmets
Sales mix	4850/6790 = 71.43%	1940/6790 = 28.57%

2) Break even point :

Weighted average contribution margin = (30*71.43%+75*28.57%) = $42.8565

Break even point = 57000/42.8565 = 1330 Units

Bicycle = 1330*71.43% = 950

Motor cycle = 1330-950 = 380

3) Contribution margin income statement

	Bicycle	Motorcycle	Total
Sales	950*77=73150	380*220 = 83600	156750
Variable cost	950*47 = 44650	380*145 = 55100	99750
Contribution margin	28500	28500	57000
Fixed cost			57000
Net operating income			0