Question

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.

Answer 1

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). $\text{Contribution margin ratio} = \frac{\text{(Sales - variable cost) }}{\text{sales}}$

                                              $=\frac{20-14}{20}$

                                             = 30%

    The Breakeven sales = $\frac{\text{fixed cost}}{\text{Contribution margin ratio}}$

                                         $=\frac{225,000}{30\%}$

                                         = 750,000

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

                                        $=\frac{1,2000,000-750,000}{1,200,000}$

                                        = 37.5%

d). Units needed :

   $(20-14)x - 225,000 = 150,000$

    $6x - 225,000 = 150,000$

    $6x = 375000$

     $x=62,500$  units

Therefore, the sales required = 62,500 x 20

                                                 = 125,000