The cost volume profit formula is used by cost accountants to demonstrate how much operating income that one of its products will produce at a particular volume. The formula can be used to determine several different production and sales goals for a company.

### CVP Formula

#### y = (ax) – (bx) – c

**y** = operating income

**ax** = (unit sales price multiplied by the number of units sold) = gross income

**bx** = (unit variable cost multiplied by the number of units sold)

**c** = fixed costs

**CVP Formula Video Tutorial With Examples**

**Number of Units Needed to Break Even**

For example a tire company may want to find out how many tires it needs to sell in order to break even each year. Solving for “units sold” in the above formula will determine the number of tires needed to break even.

The sales price for each tire is $50. The variable costs to produce each tire (rubber, metal, valves) adds up to $25.00 per tire.

The company has determined its fixed costs for the production of each tire by looking at its annual fixed overhead costs, the number of manufacturing hours it has allocated, and the amount of time needed to produce a tire.

The company spends $500,000 annually on fixed overhead costs. It has allocated 10,000 manufacturing hours per year with this amount of overhead, and each tire takes 30 minutes to produce.

To find the overhead cost per manufacturing hour, divide the annual overhead budget by the annual number of manufacturing hours.

$500,000 / 10,000 = $50.00 fixed overhead costs per manufacturing hour.

Since each tire takes 30 minutes to make, each tire costs $25.00 in fixed costs to produce. Now we have all of the numbers we need to solve the equation.

y = (ax) – (bx) – c

y = 0 (break-even point)

a = $50

x = ? (the units sold variable we are solving for)

b = $25

c = $25

0 = $50(x) – $25(x) – $25

$25 = $50(x) – $25(x)

$25 = $25(x)

$25/$25 = x

x = 1

In this example, the company’s current production methods are already perfectly breaking even at 10,000 manufacturing hours.

Since 2 tires are produced each hour, we can infer that producing 20,000 tires each year will break even for the company.

The company is right on the verge of profitability and can actually become profitable a number of ways, such as increasing their sales price slightly, reducing overhead costs slightly, or reducing the time needed to produce each tire.

As you can see, just one formula has a wide range of applications, and cost formula accounting uses hundreds of similar formulas to find valuable and insightful information on a company’s production efficiency.

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