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	$	1,300		$	700		$	80
Medium-quality		750			420			60

Three-quarters of the shop’s sales are medium-quality bikes. The shop’s annual fixed expenses are $159,600. (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 $99,750? Assume a constant sales mix.

Answer 1

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Tim’s Bicycle Shop
Workings
Calculation of contribution margin per unit	High-quality	Medium-quality	Note
Sales Price	1,300.00	750.00	A
Less:
Invoice Cost	700.00	420.00
Sales Commission	80.00	60.00
Contribution per unit	520.00	270.00	C
Calculation of sales mix	High-quality	Medium-quality	Note
Balance of units sold	1/4	3/4
Sales mix	25%	75%	D	Because 1/4 is 5% and 3/4 is 75%.

Calculation of weighted-average unit contribution margin	High-quality	Medium-quality	Total	Note
Contribution per unit	520.00	270.00		See C
Sales mix	25%	75%		See D
Weighted-average Contribution per unit	130.00	202.50	332.50	E=C*D

Calculation of break-even sales units	Total	Note
Annual fixed expenses	159,600.00	F
Weighted-average Contribution per unit	332.50	See E
Break-even sales units	480.00	G=F/E

	See A	See D	See G	I=D*G	J=A*I
Calculation of shop’s break-even sales volume in dollars	Sell Price	Sales Mix %	Total Break-even Units	Break-even Units	Sales Value
High-quality	1,300.00	25%	480.00	120.00	156,000.00
Medium-quality	750.00	75%	480.00	360.00	270,000.00
Total					426,000.00
So shop’s break-even sales volume is $ 426,000.

If target net income $ 99,750:
Calculation of target even sales units		Note
Annual fixed expenses	159,600.00
Target net income	99,750.00
Target Contribution	259,350.00	L
Weighted-average Contribution per unit	332.50	See E
Target sales units	780.00	M=L/E

	See D	See M	N=D*M
Calculation of break-even sales units- Product wise	Sales Mix %	Total Break-even Units	Break-even Units
High-quality	25%	780.00	195.00
Medium-quality	75%	780.00	585.00

So, 195 units of High-quality cycles and 585 units Medium-quality cycles should be sole to earn target net income of $ 99,750.