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Aloha Bags, Inc. produces student book bags that sell for $20 each. For the coming year, management expects fixed costs to be $225,000. Variable costs are $14 per unit.

Required:
a. Compute break-even sales in dollars using the mathematical equation.
b. Compute break-even sales using the contribution margin ratio.
c. Compute margin of safety ratio assuming actual sales are $1,200,000.
d. Compute the sales required to earn net income of $150,000, using the mathematical equation.

Sagot :

Solution :

a). At the break even units, the total contribution margin = fixed expenses

  We know that : (Selling price - variable cost) x units sold = fixed expenses  

    i.e.  (20-14)x = 225,000

                  6x   = 225,000

                    x = 37,500

Therefore, the number of units sold, x = 37,500

So, the break even analysis = 37,500 x 20

                                              = 750,000

b). [tex]$\text{Contribution margin ratio} = \frac{\text{(Sales - variable cost) }}{\text{sales}}$[/tex]

                                              [tex]$=\frac{20-14}{20}$[/tex]

                                             = 30%

    The Breakeven sales = [tex]$\frac{\text{fixed cost}}{\text{Contribution margin ratio}}$[/tex]

                                         [tex]$=\frac{225,000}{30\%}$[/tex]

                                         = 750,000

c). [tex]$\text{Margin of Safety ratio } = \frac{\text{(Sales - Breakeven sales) }}{\text{sales}}$[/tex]

                                        [tex]$=\frac{1,2000,000-750,000}{1,200,000}$[/tex]

                                        = 37.5%

d). Units needed :

   [tex]$(20-14)x - 225,000 = 150,000$[/tex]

    [tex]$6x - 225,000 = 150,000$[/tex]

    [tex]$6x = 375000$[/tex]

     [tex]x=62,500[/tex]  units

Therefore, the sales required = 62,500 x 20

                                                 = 125,000  

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