5. Gatewood Hills Corporation has three products X, Y, and Z. The company’s fixe

Question

5. Gatewood Hills Corporation has three products X, Y, and Z. The company’s fixed costs are $69,000. The sales mix for its products are 3 units of X, 4 units of Y, and 1 unit of Z. Information about the three products follows:

X

Y

Z

Projected sales in dollars

$192,000

$192,000

$64,000

Selling price per unit

$40

$30

$40

Contribution margin ratio

30%

35%

35%

Calculate the company's break-even point in composite units and sales dollars. (Hint: You will need to calculate the selling price of a composite unit and CM of a composite unit to calculate the break-even point in composite units. (2 points)

(b) Calculate the number of units of each individual product to be sold at the break-even point. (Check: At break-even point you should have 2,250 units of product X.

X

Y

Z

Projected sales in dollars

$192,000

$192,000

$64,000

Selling price per unit

$40

$30

$40

Contribution margin ratio

30%

35%

35%

Explanation / Answer

Calculation of company's break even point: Contribution margin of a composite unit= (40*0.30*3/8)+(30*0.35*4/8)+(40*0.35*1/8)                                                                                  =4.5+5.25+1.75=$11.5 Selling price of a composite unit= (40*3/8)+(30*4/8)+(40*1/8)=15+15+5=$35 Break even point (in units)=Fixed cost/contribution margin                                                        =69000/11.5= 6000 units Break even point in units=6000 units Break even point in sales dollar= 6000*35=$210000 Break even point in sales dollar=$210000 (b) Calculation of number of unit of each product to break even: Units of X= 6000*3/8=2250 units Units of Y= 6000*4/8= 3000 units Units of Z= 6000*1/8= 750 units

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