Question

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

Switzer Company produces and sells yoga-training products: how-to DVDs and a basic equipment set (blocks, strap, and small pillows). Last year, Switzer sold 10,000 DVDs and 5,000 equipment sets. Information on the two products is as follows:

	DVDs	Equipment Sets
Price	$12	$15
Variable cost per unit	4	6

Total fixed costs are $70,000.

Suppose that in the coming year, Switzer plans to produce an extra-thick yoga mat for sale to health clubs. The company estimates that 20,000 mats can be sold at a price of $18 and a variable cost per unit of $13. Fixed costs must be increased by $48,350 (making total fixed costs of $118,350). Assume that anticipated sales of the other products, as well as their prices and variable costs, remain the same.

Required:

1. What is the sales mix of DVDs, equipment sets, and yoga mats?
2:1:4

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

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

3. Prepare an income statement for Switzer for the coming year.

Switzer Company
Income Statement
For the Coming Year
Sales
Total variable cost
Contribution margin
Total fixed cost
Operating income

What is the overall contribution margin ratio? The overall break-even sales revenue? (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

Question 1

Company is expecting Sales as Follows

Particulars	DVDs	Equipment Sets	Yoga Mats
Sales	10,000	5,000	20,000
Sales Mix	2	1	4

For Every 1 Unit of Equipment Sets 2 DVDs are sold and 4 Yoga Mats are Sold so Ratio = 2:1:4.

Question 2

Particulars	DVDs	Equipment Sets	Yoga Mats
Selling Price per Unit	12	15	18
Less: Variable Costs per Unit	4	6	13
Contribution Margin per Unit	8	9	5

Calculation of Contribution Margin for Standard Sales Mix

Particulars	DVDs	Equipment Sets	Yoga Mats
Standard Sales Mix Units	2	1	4
* Contribution Margin per Unit	8	9	5
Contribution Margin	16	9	20

Total Contribution Margin = 16 + 9 + 20 = $ 45

Weighted Average Contribution Margin = Total Contribution Margin / Total Units Sold in Standard Sales Mix

Total Units Sold in Standard Sales Mix = 7

Total Contribution Margin = $ 45

Weighted Average Contribution Margin per Unit = 45 / 7

Weighted Average Contribution Margin = $ 6.43

Break Even Point in Units = Total Fixed Costs / Weighted Average Contribution Margin per Unit

Weighted Average Contribution Margin per Unit = $ 6.43

Total Fixed Costs = $ 118,350

Break Even Point in Units = 118,350 / 6.43

Break Even Point in Units = 18,410 Units

Break Even Point in Units for DVDs = 2/7 * 18,410 = 5,260 DVDs

Break Even Point in Units for Equipment Sets = 1/7 * 18,410 = 2,630 Equipment Sets

Break Even Point in Units for Yoga Mats = 4/7 * 18,410 = 10,520 Yoga Mats

Question 3

Particulars	Amount
Sales Revenue	555,000
Less: Variable Costs	(330,000)
Contribution Margin	225,000
Less: Total Fixed Costs	(118,350)
Net Operating Income / (Loss)	106,650

Sales Revenue = (10,000 DVDs * $ 12 per DVD) + (5,000 Equipment Sets * $ 15 per Equipment Sets) + (20,000 Yoga Mats * $ 18 per Yoga Mats)

= 120,000+ 75,000 + 360,000

= $ 555,000

Variable Costs = (10,000 DVDs * $ 4 per DVD) + ( 5,000 Equipment Sets * $ 6 per Equipment Sets) + (20,000 Yoga Mats * $ 13 per Yoga Mats)

= 40,000 + 30,000 + 260,000

= 330,000

Overall Contribution Margin Ratio = Total Contribution Margin / Total Sales Revenue * 100

Total Sales Revenue = $ 555,000

Total Contribution Margin = $ 225,000

Over-all Contribution Margin Ratio = 225,000 / 555,000 * 100

Overall Contribution Margin Ratio = 41%

Overall Break Even Sales in Dollars = Fixed Costs / Overall Contribution Margin Ratio

Fixed Costs = $ 118,350

Overall Contribution Margin Ratio = 41% (More Precisely 40.54% for Calculation)

Overhead Break Even Sales in Dollars = $ 291,930

Question 4

Margin of Safety Sales in Dollars = Total Sales in Dollars - Overall Break Even Sales in Dollars

Overall Break Even Sales in Dollars = $ 291,930

Total Sales in Dollars = $ 555,000

Margin of Safety Sales in Dollars = 555,000 - 291,930

Margin of Safety Sales in Dollars = $ 263,070