Sales mix, three products. The Ronowski Company has three product lines of belts—A, B, and C— with contribution margins of $3, $2, and $1, respectively. The president foresees sales of 200,000 units in the coming period, consisting of 20,000 units of A, 100,000 units of B, and 80,000 units of C. The company’s fixed costs for the period are $255,000. What is the company’s breakeven point in units, assuming that the given sales mix is maintained?
If the sales mix is maintained, what is the total contribution margin when 200,000 units are sold? What is the operating income?
What would operating income be if 20,000 units of A, 80,000 units of B, and 100,000 units of C were sold? What is the new breakeven point in units if these relationships persist in the next period?

1. 13,236 units

2. $85,000

3. $65,000

4. 15,938 units

Explanation:

First Determine the ratio of the sales mix as follows :

Ratio = 20,000 : 100,000 : 80,000

Reduced to lowest term  = 1 : 5 : 4

Then find the Company`s break-even point using the sales mix as follows ;

Break-even point (units) = Fixed Costs ÷ Contribution Margin as per sales mix

                                        = $255,000 ÷ ($3 × 1 + $2 × 5 + $1 × 4)

                                        = $255,000 ÷ $17

                                        = 13,235.29 or 13,236 units

Calculation of Operating Income assuming 200,000 units are sold

Contribution :

A : (1/10 × 200,000 units) × $3     =   $60,000

B : (5/10 × 200,000 units) × $2    = $200,000

C : (4/10 × 200,000 units) × $1     =   $80,000

Total Contribution                           $340,000          

Less Fixed Cost                             ($255,000)

Operating Income                             $85,000

Calculation of Operating Income if 20,000 units of A, 80,000 units of B, and 100,000 units of C were sold.

Contribution :

A : 20,000 units × $3      =  $60,000

B : 80,000 units × $2      = $160,000

C : 100,000 units × $1     = $100,000

Total Contribution             $320,000          

Less Fixed Cost                ($255,000)

Operating Income               $65,000

Determination of New Sales Mix :

Ratio = 20,000 : 80,000 : 100,000

Reduced to Lowest Term = 1 : 4 : 5

Break-even point (units) = Fixed Costs ÷ Contribution Margin as per sales mix

                                        = $255,000 ÷ ($3 × 1 + $2 × 4 + $1 × 5)

                                        = $255,000 ÷ $16

                                        = 15,937.5 or 15,938 units

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