Question

Texas-Q Company produces and sells barbeque grills. Texas-Q sells three models: a small portable gas grill, a larger stationary gas grill, and the specialty smoker. In the coming year, Texas-Q expects to sell 13,800 portable grills, 50,600 stationary grills, and 4,600 smokers. Information on the three models is as follows:

	Portable	Stationary	Smokers
Price	$89	$204	$253
Variable cost
per unit	50	134	143

Total fixed cost is $2,163,490.

	Required:
1.	What is the sales mix of portable grills to stationary grills to smokers?
2.	Compute the break-even quantity of each product.
3.	Prepare an income statement for Texas-Q for the coming year. What is the overall contribution margin ratio? Use the contribution margin ratio to compute overall break-even sales revenue. Enter the contribution margin ratio as a percentage rounded to two decimal places; round the break-even sales revenue to the nearest dollar.
4.	Compute the margin of safety for the coming year.

Answer 1

1 SALES MIX

Total unit produced by Texas-Q

= 13,800 + 50,600 + 4,600 = 69,000 units

Portable sales mix = (13,800 / 69,000) × 100 = 20%

Stationary sales mix = (50,600 / 69,000) × 100 = 73.33%

Smokers sales mix = (4,600 / 69,000) × 100 = 6.67%

2 total break even quantity of Texas-Q

= fixes cost / weighted average contribution margin

Weighted average contribution margin

= contribution margin of each product × sales mix of each product

Contribution margin = sales - variable cost

CONTRIBUTION MARGIN OF PRODUCTS

Portable = 89 - 50 = 39

Stationary = 204 - 134 = 80

Smokers = 253 - 143 = 110

Fixed cost = $2,163,490

Weighted average contribution margin

= (39 × 20%) + (80 × 73.33%) + (110 × 6.67%) = 73.801

total break even quantity of Texas-Q

= 2,163,490 / 73.801 = 29,315 units

BREAK EVEN QUANTITY FOR EACH PRODUCTS

The following are the break even quantity for each products

Portable = 29,315 × 20% = 5,863 units

Stationary = 29,315 × 73.33% = 21,497 units

Smokers = 29,315 × 6.67% = 1,995 units

3 income statement of Texas-Q

Particulars	$
Sales (89×13,800) + (204 × 50,600) + (253 × 4,600)	12,714,400
Less variable cost (50 × 13,800) + (134 × 50,600) + (143 × 4,600)	8,128,200
Contribution margin	4,586,200
Less fixed cost	2,163,490
Operating profit	2,422,710

Overall contribution margin ratio

= (4,586,200 / 12,714,400) × 100 = 36.07%

Overall break even sales revenue

= 2,163,490 / 36.07% = $5,998,032

4 Margin of safety = actual sales - break even sales

Margin of safety = 12,714,400 - 5,998,032 = $6,716,368

The margin of safety of Texas-Q is $6,716,368.

The above are the detailed calculations.

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