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

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

`$=(20-14)/(20)$`

= 30%

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

`$=(225,000)/(30\%)$`

= 750,000

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

`$=(1,2000,000-750,000)/(1,200,000)$`

= 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