Question

A company sells two models of a product—basic and premium. The basic model has a variable cost of $75 and sells for $100. The premium model has a variable cost of $100 and sells for $150. Fixed costs are $15,000. If the company usually sells 5,000 basic models and 2,500 premium models, then the break-even point in composite units is _________ units.

What are the steps?

Answer 1

Answer:

Beak-even point  =   450 units

                 

Explanation:

The break-even point is the level of activity where a business makes no profit or loss. At this level of activity, the total contribution equals the total  fixed costs.

To calculate the break even point in a multi product scenario, we use the formula below:

Break-even point = Fixed cost for the period / average contribution per unit

Average contribution per unit = Total contribution in a mix/ units in a mix

We will follow the steps below to work out the Break-even point:

Step 1

Calculate the average contribution per unit

contribution per unit for each product= selling price - variable cost

Basic model = 100- 75 = $25

Premium model =  150 - 100 = $50

Average contribution per unit = ( 5000 × $25) + (2500 × $50)

                                                            (   5000 + 2500) units

                                = $33.33 per unit

Step 2

Calculate the Break-even point

Break even point = $15,000/ $33.33

                           =   450 units

Answer 2

Answer:

BEP MIX = 450

Explanation:

$\frac{Fixed\:Cost}{Contribution \:Margin} = Break\: Even\: Point_{units}$

Where:

$Sales \: Revenue - Variable \: Cost = Contribution \: Margin$

The contribution represent the value of the sale after deducting the cost to generate the sale:

Item A

100 - 75 = 25 dollars

Item B

150 - 100 = 50 dollars

The unit sales ratio is 5,000:2,500 which is 2:1

Thus:

25 x 2/3

+ 50 x 1/3

contribution of the mix:

33.33333333

Now we return to the break even point formula:

$\frac{Fixed\:Cost}{Contribution \:Margin} = Break\: Even\: Point_{units}$

$\frac{15,000}{33.33} = Break\: Even\: Point_{units}$

BEP = 450