## 3.3. Contribution margin technique in CVP analysis

Earlier we calculated the sales required for desired profits by using the equation technique. We will now calculate such sales by using the contribution margin technique.

Let's go back to our contribution margin equation:

Contribution Margin = Sales - Variable Costs

We also know the following:

Sales - Variable Costs = Fixed Costs + Profits

If we replace Sales - Variable Costs in the first equation with Fixed Costs + Profits from the second equation, we will have the following result:

Contribution Margin = Fixed Costs + Profits

Contribution margin can also be presented as:

Contribution Margin = Contribution Margin per Unit x Units Sales

Finally, if we combine the contribution margin per unit with Fixed Assets + Profits, we obtain the following:

Contribution Margin per Unit x Unit Sales = Fixed Costs + Profits

Therefore, a required unit sales for a given desired profit can be calculated as follows:

 Unit Sales = Fixed Costs + Target Profit Contribution Margin per Unit

In our example of Friends Company, we can calculate sales volume (in units) necessary to gain the desired profit of \$30,000 as follows:

 Unit Sales = \$10,000 + \$30,000 = 20,000 units \$2

In the same manner, we can calculate the unit sales necessary to gain the desired profit of \$40,000:

 Unit Sales = \$10,000 + 40,000 = 25,000 units \$2

We can also calculate the amount of sales in dollars. We will apply a similar formula, except that instead of Contribution Margin per Unit we will use Contribution Margin Ratio:

Contribution Margin Ratio x Sales = Fixed Costs + Profits

After some rearrangements to this equation, we come to the following one:

 Sales (dollars) = Fixed Costs + Target Profit Contribution Margin Ratio

Let's determine required sales in dollars to generate \$30,000 in profits:

 Sales (dollars) = \$10,000 + \$30,000 = \$100,000 40%

Note that required sales for the \$30,000 desired profit can also be calculated by multiplying the required unit sales by the selling price per unit: 20,000 x \$5 = \$100,000. Also note that the \$100,000 matches the required sales we calculated before using the equation technique.

The calculation for the \$40,000 desired profit is as follows:

 Sales (dollars) = \$10,000 + \$40,000 = \$125,000 40%

Again, the required sales for the \$40,000 desired profit can also be calculated by multiplying the required unit sales by the selling price per unit: 25,000 x \$5 = \$125,000. This amount once again agrees with the required sales calculated by using the equation technique.

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