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5 January, 08:54

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?

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  1. 5 January, 12:31
    0
    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
  2. 5 January, 12:49
    0
    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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