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	$	1,800		$	950			$	40
Medium-quality		1,000			670				20

Three-quarters of the shop’s sales are medium-quality bikes. The shop’s annual fixed expenses are $234,900. (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 $130,500? Assume a constant sales mix.

Answer 1

1. Contribution Margin = Sales Price - Variable Costs
High-Quality = $1800 - 990 = $810
Medium-Quality = $1000 - 690 = $310

2.
Shops Sales Mix = 1 unit of High Quality for 3 units of Medium Quality product

3.
Weighted Average Unit Contribution Margin = (1 x $810 + 3 x $310) / 4 = $435 per unit

4.
Break even sales (units) = Fixed Costs / Weighted Average Unit Contribution Margin
= $234900 / 435 = 540 units

High Quality = 540 x 1/4 = 135 units
Medium Quality = 540 x 3/4 = 405 units

Break even sales (dollars) = 135 x $1800 + 405 x 1000 = $648,000

5.
Units to be sold = (Fixed Costs + Target Income) / Weighted Average Unit Contribution Margin
= ($234900+130500) / 435 = 840 units

High Quality = 840 x 1/4 = 210 units
Medium Quality = 840 x 3/4 = 630 units

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