Question

Multiple-Product Break-even, Break-Even Sales Revenue

Cherry Blossom Products Inc. produces and sells yoga-training products: how-to DVDs and a basic equipment set (blocks, strap, and small pillows). Last year, Cherry Blossom Products sold 13,500 DVDs and 4,500 equipment sets. Information on the two products is as follows:

	DVDs	Equipment Sets
Price	$8	$25
Variable cost per unit	4	15

Total fixed cost is $77,270.

Suppose that in the coming year, the company plans to produce an extra-thick yoga mat for sale to health clubs. The company estimates that 9,000 mats can be sold at a price of $17 and a variable cost per unit of $11. Total fixed cost must be increased by $25,750 (making total fixed cost $103,020). Assume that anticipated sales of the other products, as well as their prices and variable costs, remain the same.

Part 1: Sales Mix Instructions and Part 2: Break-Even

1. What is the sales mix of DVDs, equipment sets, and yoga mats?
3:1:2

2. Compute the break-even quantity of each product.

Break-even DVDs	units
Break-even equipment sets	units
Break-even yoga mats	units

3a. Prepare an income statement for Cherry Blossom Products for the coming year. Cherry Blossom Products Inc. Income Statement For the Coming Year $ $ $

3b. What is the overall contribution margin ratio? Use the contribution margin ratio to compute overall break-even sales revenue. (Note: Round the contribution margin ratio to the nearest whole percent; round the break-even sales revenue to the nearest dollar.)

Overall contribution margin ratio		%
Overall break-even sales revenue	$

4. Compute the margin of safety for the coming year in sales dollars.
$

Answer 1

1. Sales mix = 13500 : 4500 : 9000 = 3 : 1 : 2

2.

Break-even DVDs	9085	units
Break-even equipment sets	3028	units
Break-even yoga mats	6056	units

Note: The units have been rounded off to the nearest whole number in the absence of instructions regarding the same. The answers could vary due to the rounding off. Kindly mention in the comments section in case there is any difference that needs to be resolved.

Workings:

	DVDs	Equipment Sets	Yoga Mats	Total
Selling price per unit $	8	25	17
Variable cost	4	15	11
Contribution per unit $	4	10	6
x Sales Mix (3 : 1 : 2)	3	1	2	6
Total contribution	12	10	12	34
Weighted average contribution per unit ($34/6)				5.67

Total break-even quantity = Total fixed costs/Weighted average contribution margin per unit = $103020/$5.67 = 18169 units

DVDs = 3/6 x 18169 = 9085 units

Equipment sets = 1/6 x 18169 = 3028 units

Yoga mats = 2/6 x 18169 = 6056 units

3a.

Cherry Blossom Products Inc.,
Income Statement
For the Coming Year
Sales revenue	373500
Variable expenses	220500
Contribution margin	153000
Fixed expenses	103020
Net operating income $	49980

3b.

Overall contribution margin ratio	41	%
($153000/$373500)
Overall break-even sales revenue $	251268
($103020/41%)

4. Margin of safety = Expected sales - Break-even sales = $373500 - $251268 = $122232