## 2.2. Equation technique in CVP analysis

We just saw how to calculate the volume of minimum sales in units and dollars to break-even (i.e., have zero profits). What if we want to know how many valves need to be sold to earn a \$30,000 profit? What about a \$40,000 profit?

The answer can be found by using the same equation we used before:

Sales = Variable Costs + Fixed Costs + Profits

Note that:

Sales = Sales Price per Unit x Unit Sales

Variable Costs = Variable Cost per Unit x Unit Sales

If we replace Sales and Variable Costs in the equation, we will get the following result:

Selling Price per Unit x Unit Sales = Variable Costs per Unit x Unit Sales + Fixed Costs + Profits

When we further re-arrange the equation, we will obtain the following:

 Unit Sales = Fixed Costs + Profits Selling Price per Unit - Variable Costs per Unit

Using this formula, we can calculate how many units should be sold to generate \$30,000 in profits for Friends Company:

 Unit Sales = \$10,000 + \$30,000 = 20,000 units \$5 - \$3

The same formula can be used when the target profit is \$40,000:

 Unit Sales = \$10,000 + \$40,000 = 25,000 units \$5 - \$3

The 20,000 and 25,000 units can be converted to dollars as follows: \$100,000 (\$5 x 20,000 units) and \$125,000 (\$5 x 25,000 units), respectively.

We can check our answers for the desired \$30,000 and \$40,000 profits by using the same formula we applied before:

Profits = Selling Price per Unit x Unit Sales - Variable Costs per Unit x Unit Sales - Fixed Costs

For the 20,000 units sold, the profits will be calculated as follows:

Profits = \$5 x 20,000 - \$3 x 20,000 - \$10,000 = \$30,000

And for the 25,000 units sold, the profits can be determined as shown below:

Profits = 25,000 x \$5 - 25,000 x \$3 - 10,000 = \$40,000

In both cases, we arrived at the desired level of profits and this proves that our calculations were correct.

Now when we know that we've got to sell 20,000 units (or generate \$100,000 in sales) to earn the \$30,000 profits and 25,000 units (or \$125,000) to make \$40,000 of profits, Friends Company can assess (a) if it is possible considering the market situation; (b) what level of sales is more realistic in the company's situation; (c) what amount of resources the company needs; and (d) if Friends Company needs to hire more employees to generate a desired level of profits.

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