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# Cost-volume-profit (CVP) analysis

Published on April 1, 2018   23 min
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#### Other Talks in the Series: Management Accounting

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Hello, everyone. I would like to welcome you to this HS Talks lecture series on Managerial Accounting. My name is Alexander Himme, and I'm an Assistant Professor from Managerial Accounting at the Kuhne Logistics University in Hamburg, Germany. In this module, we will talk about "Cost-Volume-Profit Analysis". Cost-volume-profit analysis is also often called break-even analysis. It is a planning tool that looks at the relationships among costs and volumes and how they affect profits. Again, for an understanding of this module, it is important that you recall the contents of Module Number 2. Here, we talked about different cost categories, especially variable and fixed costs and the contribution margin.
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Before we look in detail how we apply the cost-volume-profit analysis, let us make some assumptions. These assumptions make our life easier when it comes to the following calculations on the next slides. They are also the typical assumptions that managers make when they conduct cost-volume-profit analysis. We can relax these assumptions, but this would severely complicate the issue. There are six assumptions that are made within the cost-volume-profit analysis. First, the price per unit does not change as volume changes. That means we assume in linear sales function that every unit more that we sell results in a constant increase of total sales. The setting price per unit is typically constant in the relevant range. Only if you start to sell huge amounts and then allow for discounts, prices would not be constant anymore. Second, managers can classify each cost as variable or fixed via following the high-low method in Module number 2. So, this method is applied to determine variable and fixed cost in the case of mixed cost. Third, we assume that the production volume is the only factor that affects variable and mixed costs. Changes in other variables, like production efficiency, that may influence costs are not considered. Since volume is typically the main cost driver, this assumption is not very strict. But, of course, if there are significant changes in production efficiency, then you should not apply the cost-volume-profit analysis. Fourth, like for the price, we assume that variable cost per unit does not change. Again, this implies that we are not in a situation where a firm produces huge amounts of products and then because of that, the company receives quantity discounts for direct materials, which in turn would change the variable cost per unit. Fifth, it is assumed that fixed costs do not change. In other words, recall Module 2, the company is in the relevant range where it does not change overall capacities. In general, the cost-volume-profit analysis should always only be applied within the relevant range. Finally, the sixth assumption is probably the most severe one. We assume that there are no changes in inventory levels. This implies that the number of units produced always equals the number of units sold. Otherwise, the unit costs depend on the inventory levels and would not be constant. Then, we cannot apply the cost-volume-profit analysis. We agree that most business conditions do not perfectly meet these general assumptions. As a result, you as a manager should always regard cost-volume-profit analysis as a proxy, not as a 100 percent exact calculation. But, in general, within the relevant range, these linear relationships are realistic and good proxies of actual cost and revenue behavior. It also represents the area where the firm has experience and knows the cost behavior. So in other words, the cost-volume-profit analysis is a planning tool for the short run. The costs and revenues per unit are constant. In the long run, variable and fixed costs, as well as prices per unit, may change. Then the assumptions of the cost-volume-profit analysis must be carefully checked if they still hold. The cost-volume-profit analysis can be applied in three different ways: the equation approach, the contribution margin approach, and the contribution margin ratio approach. Let us look at each in detail by using examples.
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