Question

Tim’s Bicycle Shop sells 21-speed bicycles. For purposes of a cost-volume-profit analysis, the shop owner has divided sales into two categories, as follows:

Product Type	Sales Price			Invoice Cost			Sales Commission
High-quality	$	1,400		$	750		$	90
Medium-quality		800			470			70

Three-quarters of the shop’s sales are medium-quality bikes. The shop’s annual fixed expenses are $147,400. (In the following requirements, ignore income taxes.)

Required:

1. Compute the unit contribution margin for each product type.

2. What is the shop’s sales mix?

3. Compute the weighted-average unit contribution margin, assuming a constant sales mix.

4. What is the shop’s break-even sales volume in dollars? Assume a constant sales mix.

5. How many bicycles of each type must be sold to earn a target net income of $100,500? Assume a constant sales mix.

Compute the unit contribution margin for each product type.

	Bicycle Type Unit Contribution Margin High-quality Medium-quality

What is the shop’s sales mix?

	Bicycle Type Sales Mix High-quality % Medium-quality %

Compute the weighted-average unit contribution margin, assuming a constant sales mix. (Round your answer to 1 decimal place.)

	Weighted-average unit contribution margin

What is the shop’s break-even sales volume in dollars? Assume a constant sales mix.

	Break-even sales volume

How many bicycles of each type must be sold to earn a target net income of $100,500? Assume a constant sales mix.

	Bicycle Type Number of Bicycles High-quality Medium-quality

Answer 1

1)	unit contribution margin					unit
			Sales	invoice	Sales	Contribution
			price	cost	commission	margin
	High-quality		1,400	750	90	560
	Medium quality		800	470	70	260
2)	Bicyle type		Sales-mix
	High-quality		25%
	Medium quality		75%
3)	Weighted -average unit contribution margin				335.0
	(560*25%+260*75%)
4)	Break even sales volume				418000
	BEP(units)=		fixed cost/weighted contribution margin
			147,400/335
			440	units
			divide 440 units in the ratio of sales mix
			units	selling price	total
	High-quality		110	1,400	154000
	Medium quality		330	800	264000
	total				418000
5)	BEP(units)=		(fixed cost+target income)/weighted contribution margin
			(147,400+100500)/335
			740	units
	Bicycle type		number of bicylces
	High-quality		185
	Medium quality		555