## 3.2. Contribution margin technique in CVP analysis and break-even point

Now that we know what contribution margin and contribution margin ratio are we can use them in CVP analysis to calculate the break-even point for our Friends Company example. Recall that break-even is a situation when profits equal zero. This means that contribution in this case equals fixed costs only:

Contribution = Fixed Costs + Profits = Fixed Costs + 0 = Fixed Costs

To calculate the break-even point in units, we can use the following formula:

 Break-even Sales in Units = Fixed Costs Contribution per Unit

Recall that contribution contributes toward (covers) fixed costs. Based on this, the equation above can also be read as "How many units do we need to sell to cover all fixed costs and have zero profit?"

To calculate the break-even point in dollars, we will use a similar formula, but will now apply the contribution margin ratio:

 Break-even Sales in Dollars = Fixed Costs Contribution Margin Ratio

The equation above can also be read as "How much sales, in dollars, do we need to generate to cover all fixed costs and have zero profit?"

Using these break-even formulas, the break-even sales for Friends Company can be computed as follows:

 Break-even Sales in Units = \$10,000 = 5,000 units \$2

If the company sells 5,000 units, it has neither loss nor profit. We can check this calculation by determining the profit when 5,000 units are sold:

Profits = Sales - Variable Costs - Fixed Costs = 5,000 x \$5 - 5,000 x \$3 - \$10,000 = 0

The company will suffer a loss if it sells fewer than 5,000 units and will generate profit if the sales exceed 5,000 units.

The amount of break-even sales in dollars can be determined as shown below:

 Break-even Sales in Dollars = \$10,000 = \$25,000 40%

The break-even sales in dollars can also be determined by multiplying the 5,000 units for break-even by the selling price per unit: 5,000 x \$5 = \$25,000. As you can see, the result is the same (i.e., \$25,000).

Note that the break-even sales in units and dollars calculated by using the contribution margin technique equal the break-even units and dollars determined by the equation technique.

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