Friar Corp. sells two products. Product A sells for $100 per unit, and has unit variable costs of $60. Product B sells for $70 per unit, and has unit variable costs of $50. Currently, Friar sells three units of product B for every one unit of product A sold. Friar has fixed costs of $750,000. How many units would Friar have to sell to earn a profit of $250,000?

Explanation:

Sales in units =

(Total fixed cost+Required profit)/(Weighted average Contribution Margin) = (750,000+250,000)/25 = 1,000,000/25 = 40,000

In order to earn profit of $250,000 Friar needs to sell 40,000 units

*Weighted average Contribution Margin = [(100-60)*1/4] + [(70-50)*3/4] = 10+15 = 25

40,000 units

Explanation:

We can proceed as follows:

CMA = Contribution margin of A = $100 - $60 = $40

CMB = Contribution margin of B = $70 - $50 = $20

Unit of A sold with B = 1

Unit of B sold with A = 3

Unit of A and B sold together at a time = 1 + 3 = 4

WA = Weight of A in the sales combination = 1/4  

WB = Weight of B in the sales combination= 3/4

Weighted average unit contribution margin = (CMA × WA] + (CMB × WB)

                                                                        = ($40 × 1/4) + (20 × 3/4)

                                                                        = $10 + $15

Weighted average unit contribution margin = $25

Target units = (Fixed cost + Targeted profit) ÷ Weighted average unit contribution margin

                    = ($750,000 + $250,000) ÷ $25

                    = $1,000,000 ÷ 25

Target units = 40,000 units.

Therefore, Friar would have to sell 40,000 units to earn a profit of $250,000.

Note:

Note that the 40,000 units are for products A and B and it can be divided for them based on their weights as follows:

Units of Product A = 40,000 × 1/4 = 10,000 units

Units of Product B = 40,000 × 3/4 = 30,000 units.

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