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	$	1,150		$	490		$	70
Medium-quality		570			270			60

Three-quarters of the shop’s sales are medium-quality bikes. The shop’s annual fixed expenses are $196,500. (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 $98,250? Assume a constant sales mix.

Answer 1

SOLUTION:

1)CONTRIBUTION MARGIN PER UNIT:

PRODUCT TYPE-HIGH QUALITY

CONTRIBUTION=SALES PRICE-VARIABLE COST

=1150-(490+70)=1150-560=$590

PRODUCT TYPE MEDIUM QUALITY

CONTRIBUTION=SALES PRICE-VARIABLE COST

=570-(270+60)=570-330=$240

2)SHOP'S SALES MIX:

THREE QUARTERS OF THE SHOP,S SALES ARE MEDIUM QUALITY BIKES, THEREFORE 3/4*100=75%

MEDIUM QUALITY 75%

HIGH QUALITY 25%

3)WEIGHTED AVERAGE CONTRIBUTION MARGIN=(590*25%)+(240*75%)

=147.5+180 =$327.5

4)SHOP'S BREAK EVEN SALES VOLUME IN DOLLARS=ANNUAL FIXED EXPENSE/WEIGHTED AVERAGE CONTRIBUTION MARGIN

=196500/327.5 =600 BICYCLES

BICYCLE TYPE	BREAK EVEN VOLUME	SALES PRICE	SALES REVENUE
HIGH QUALITY	150(600*25%)	1150	172500
MEDIUM QUALITY	450(600*75%)	570	256500
BREAK EVEN SALES IN DOLLARS	429000

5)SALES VOLUME REQUIRED TO EARN TARGET PROFIT=(FIXED COST+TARGET PROFIT)/WEIGHTED AVERAGE CONTRIBUTION MARGIN PER UNIT

=196500+98250/327.5

=294750/327.5

900 BICYCLES

HIGH QUALITY BICYCLE TYPE=900*25%=225 BICYCLES

MEDIUM QUALITY BICYCLE TYPE=900*75% =675 BICYCLES