In this lesson, we’ll explore cost-volume profit analysis, which companies use to help them figure out how many products to make, and at how much to sell them for in order to make their desired profit. We’ll also discuss contribution margins.

## Definition of Cost-Volume-Profit Analysis

Chances are that you didn’t get into business just because you didn’t have anything better to do. No, you wanted to make a profit! However, unless you happen to find a shrub that grows dollar bills, you know the old adage that money doesn’t grow on trees. Instead, you have to spend money to make money, since raw materials have cost.

And chances are, you’re not interested in just making one of something.So when do you know when you’ve made enough of your products to make a profit? And how should you price your goods in order to make a desired profit? Luckily for you, there’s something called a cost-volume-profit analysis for figuring this out. While this may sound intimidating, the concept is relatively straightforward.

## Formula for Cost-Volume-Profit Analysis

In fact, there’s even a formula to help you completely understand how to use **cost-volume-profit analysis**. It’s:*xp = xv + FC + profit*But what does it all mean?

- The
*x*stands for number of units sold - The
*p*stands for price per unit sold - The
*v*stands for variable cost per unit sold *FC*stands for overall fixed costs- Finally,
*profit*is the amount of money that you want to make selling these goods.

Remember that **variable costs** are costs that go up with each extra unit of production, like raw materials, while **fixed costs** are costs that are set, and not dependent on production, like the property taxes on a factory.

Let’s walk through a quick example. Say that you wanted to make $100,000 by selling 10,000 widgets. The fixed cost is $200,000, while the variable cost per widget is $20.

Let’s plug those numbers into our formula:10,000*p* = (10,000)($20) + $200,000 + $100,000Simplifying it a bit, we get this:10,000*p* = $500,000*p* = $50In other words, we have to sell each widget for $50 to make our desired profit.

## Contribution Margin and CM Ratio

The **contribution margin** is the total revenue minus all variable costs. It realizes that fixed costs can be paid back over time. It’s why the ice cream truck doesn’t charge $50,000 for the first ice cream cone it ever sells.

More often than not, the total contribution margin is the number used for income statements.Sometimes, instead of the total contribution margin, we may need to know the per unit contribution margin, in order to figure out if we are reaching a point of diminishing returns. This would be useful in helping us make sure that our prices are high enough, for example. To find the price per unit contribution margin, we subtract the variable cost per unit from the price of the unit. For example, if a widget had a price of $50, and a variable cost per unit of $20, then the per unit contribution margin would be $30.

Finally, we may sometimes want to know the **contribution margin ratio**, which gives us an idea of what portion of our total sales makes up the contribution margin. To do this, we divide the contribution margin by the total sales. For example, let’s say we wanted to find the contribution margin ratio for the example in the previous section. First, we need to figure out the contribution margin. Remember, $500,000 was the total sales (10,000 units X $50 per unit).

So, $500,000 (total sales) – $200,000 (variable costs), would give us our contribution margin of $300,000. From there, we would divide this number by total sales ($300,000 / $500,000), giving us a contribution margin ratio of 0.6.

## Lesson Summary

A **cost-volume-profit analysis** helps a company decide how many products it needs to make, and at what price to sell them, in order to make a desired profit. The formula for this analysis is:*xp = vx + FC + profit*Remember that *x* stands for number of units, *p* stands for price per unit, *v* stands for variable cost per unit, and *FC* stands for fixed cost. **Variable costs** are those costs that increase with each additional unit made, while **fixed costs** stay the same no matter how many units are made.

Finally, we learned how to calculate the contribution margin and the contribution margin ratio. The **contribution margin** is the total revenue minus total variable costs, while the **contribution margin ratio** is the contribution margin divided by total revenue.