case study on cost volume profit analysis

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Cost-volume-profit analysis looks primarily at the effects of differing levels of activity on the financial results of a business

In any business, or, indeed, in life in general, hindsight is a beautiful thing. If only we could look into a crystal ball and find out exactly how many customers were going to buy our product, we would be able to make perfect business decisions and maximise profits.

Take a restaurant, for example. If the owners knew exactly how many customers would come in each evening and the number and type of meals that they would order, they could ensure that staffing levels were exactly accurate and no waste occurred in the kitchen. The reality is, of course, that decisions such as staffing and food purchases have to be made on the basis of estimates, with these estimates being based on past experience.

While management accounting information can’t really help much with the crystal ball, it can be of use in providing the answers to questions about the consequences of different courses of action. One of the most important decisions that need to be made before any business even starts is ‘how much do we need to sell in order to break-even?’ By ‘break-even’ we mean simply covering all our costs without making a profit.

This type of analysis is known as ‘cost-volume-profit analysis’ (CVP analysis) and the purpose of this article is to cover some of the straight forward calculations and graphs required for this part of the Performance Management syllabus, while also considering the assumptions which underlie any such analysis.

The objective of CVP analysis

CVP analysis looks primarily at the effects of differing levels of activity on the financial results of a business. The reason for the particular focus on sales volume is because, in the short-run, sales price, and the cost of materials and labour, are usually known with a degree of accuracy. Sales volume, however, is not usually so predictable and therefore, in the short-run, profitability often hinges upon it. For example, Company A may know that the sales price for product X in a particular year is going to be in the region of $50 and its variable costs are approximately $30.

It can, therefore, say with some degree of certainty that the contribution per unit (sales price less variable costs) is $20. Company A may also have fixed costs of $200,000 per annum, which again, are fairly easy to predict. However, when we ask the question, ‘Will the company make a profit in that year?’ the answer is ‘We don’t know’. We don’t know because we don’t know the sales volume for the year. However, we can work out how many sales the business needs to achieve in order to make a profit and this is where CVP analysis begins.

Methods for calculating the break-even point The break-even point is when total revenues and total costs are equal, that is, there is no profit but also no loss made. There are three methods for ascertaining this break-even point: 

(1) The equation method A little bit of simple maths can help us answer numerous different cost‑volume-profit questions.

We know that total revenues are found by multiplying unit selling price (USP) by quantity sold (Q). Also, total costs are made up firstly of total fixed costs (FC) and secondly by variable costs (VC). Total variable costs are found by multiplying unit variable cost (UVC) by total quantity (Q). Any excess of total revenue over total costs will give rise to profit (P). By putting this information into a simple equation, we come up with a method of answering CVP type questions. This is done below continuing with the example of Company A above.

Total revenue – total variable costs – total fixed costs = Profit (USP x Q) – (UVC x Q) – FC = P (50Q) – (30Q) – 200,000 = P

Note: total fixed costs are used rather than unit fixed costs since unit fixed costs will vary depending on the level of output.

It would, therefore, be inappropriate to use a unit fixed cost since this would vary depending on output. Sales price and variable costs, on the other hand, are assumed to remain constant for all levels of output in the short-run, and, therefore, unit costs are appropriate.

Continuing with our equation, we now set P to zero in order to find out how many items we need to sell in order to make no profit, i.e. to break even:

(50Q) – (30Q) – 200,000 = 0 20Q – 200,000 = 0 20Q = 200,000 Q = 10,000 units.

The equation has given us our answer. If Company A sells less than 10,000 units, it will make a loss. If it sells exactly 10,000 units it will break-even, and if it sells more than 10,000 units, it will make a profit.

(2) The contribution margin method This second approach uses a little bit of algebra to rewrite our equation above, concentrating on the use of the ‘contribution margin’. The contribution margin is equal to total revenue less total variable costs. Alternatively, the unit contribution margin (UCM) is the unit selling price (USP) less the unit variable cost (UVC). Hence, the formula from our mathematical method above is manipulated in the following way:

(USP x Q) – (UVC x Q) – FC = P (USP – UVC) x Q = FC + P UCM x Q = FC + P Q = FC + P         UCM

So, if P = 0 (because we want to find the break-even point), then we would simply take our fixed costs and divide them by our unit contribution margin. We often see the unit contribution margin referred to as the ‘contribution per unit’.

Applying this approach to Company A again:

UCM = 20, FC = 200,000 and P = 0. Q = FC      UCM Q = 200,000            20

Therefore, Q = 10,000 units

The contribution margin method uses a little bit of algebra to rewrite our equation above, concentrating on the use of the ‘contribution margin’.

(3) The graphical method With the graphical method, the total costs and total revenue lines are plotted on a graph; $ is shown on the y axis and units are shown on the x axis. The point where the total cost and revenue lines intersect is the break-even point. The amount of profit or loss at different output levels is represented by the distance between the total cost and total revenue lines.  Figure 1  shows a typical break-even chart for Company A. The gap between the fixed costs and the total costs line represents variable costs.

Alternatively, a contribution graph could be drawn. While this is not specifically covered by the Performance Management syllabus, it is still useful to see it. This is very similar to a break-even chart; the only difference being that instead of showing a fixed cost line, a variable cost line is shown instead.

Hence, it is the difference between the variable cost line and the total cost line that represents fixed costs. The advantage of this is that it emphasises contribution as it is represented by the gap between the total revenue and the variable cost lines. This is shown for Company A in  Figure 2 .

Finally, a profit–volume graph could be drawn, which emphasises the impact of volume changes on profit ( Figure 3 ). This is key to the Performance Management syllabus and is discussed in more detail later in this article.

Ascertaining the sales volume required to achieve a target profit

As well as ascertaining the break-even point, there are other routine calculations that it is just as important to understand. For example, a business may want to know how many items it must sell in order to attain a target profit.

Example 1 Company A wants to achieve a target profit of $300,000. The sales volume necessary in order to achieve this profit can be ascertained using any of the three methods outlined above. If the equation method is used, the profit of $300,000 is put into the equation rather than the profit of $0:

(50Q) – (30Q) – 200,000 = 300,000 20Q – 200,000 = 300,000 20Q = 500,000 Q = 25,000 units.

Alternatively, the contribution method can be used:

UCM = 20, FC = 200,000 and P = 300,000. Q = FC + P         UCM Q = 200,000 + 300,000                   20

Therefore, Q = 25,000 units.

Finally, the answer can be read from the graph, although this method becomes clumsier than the previous two. The profit will be $300,000 where the gap between the total revenue and total cost line is $300,000, since the gap represents profit (after the break-even point) or loss (before the break-even point.)

A contribution graph shows the difference between the variable cost line and the total cost line that represents fixed costs. An advantage of this is that it emphasises contribution as it is represented by the gap between the total revenue and variable cost lines.

This is not a quick enough method to use in an exam so it is not recommended.

Margin of safety The margin of safety indicates by how much sales can decrease before a loss occurs – ie it is the excess of budgeted revenues over break-even revenues. Using Company A as an example, let’s assume that budgeted sales are 20,000 units. The margin of safety can be found, in units, as follows:

Budgeted sales – break-even sales = 20,000 – 10,000 = 10,000 units.

Alternatively, as is often the case, it may be calculated as a percentage:

(Budgeted sales – break-even sales)/budgeted sales

In Company A’s case, it will be (10,000/20,000) x 100 = 50%.

Finally, it could be calculated in terms of $ sales revenue as follows:

(Budgeted sales – break-even sales) x selling price = 10,000 x $50 = $500,000.

Contribution to sales ratio It is often useful in single product situations, and essential in multi‑product situations, to ascertain how much each $ sold actually contributes towards the fixed costs. This calculation is known as the contribution to sales or C/S ratio. It is found in single product situations by either simply dividing the total contribution by the total sales revenue, or by dividing the unit contribution margin (otherwise known as contribution per unit) by the selling price:

For Company A: ($20/$50) = 0.4

In multi-product situations, a weighted average C/S ratio is calculated by using the formula:

Total contribution/total sales revenue

This weighted average C/S ratio can then be used to find CVP information such as break-even point, margin of safety, etc.

Example 2 As well as producing product X described above, Company A also begins producing product Y. The following information is available for both products:

The weighted average C/S ratio of 0.34375 or 34.375% has been calculated by calculating the total contribution earned across both products and dividing that by the total revenue earned across both products.

The C/S ratio is useful in its own right as it tells us what percentage each $ of sales revenue contributes towards fixed costs; it is also invaluable in helping us to quickly calculate the break-even point in $ sales revenue, or the sales revenue required to generate a target profit. The break-even point in sales revenue can now be calculated this way for Company A:

Fixed costs/contribution to sales ratio = $200,000/0.34375 = $581,819 of sales revenue.

To achieve a target profit of $300,000:

(Fixed costs + required profit)/contribution to sales ratio = ($200,000 + $300,000)/0.34375 = $1,454,546.

Of course, such calculations provide only estimated information because they assume that products X and Y are sold in a constant mix of 2X to 1Y. In reality, this constant mix is unlikely to exist and, at times, more Y may be sold than X. Such changes in the mix throughout a period, even if the overall mix for the period is 2:1, will lead to the actual break-even point being different than anticipated. This point is touched upon again later in this article.

Contribution to sales ratio is often useful in single product situations, and essential in multi‑product situations, to ascertain how much each $ sold actually contributes towards the fixed costs.

Multi-product profit–volume charts

When discussing graphical methods for establishing the break-even point, we considered break-even charts and contribution graphs. These could also be drawn for a company selling multiple products, such as Company A in our example.

The one type of graph that hasn’t yet been discussed is a profit–volume graph. This is slightly different from the others in that it focuses purely on showing a profit/loss line and doesn’t separately show the cost and revenue lines. In a multi‑product environment, it is common to actually show two lines on the graph: one straight line, where a constant mix between the products is assumed; and one bow-shaped line, where it is assumed that the company sells its most profitable product first and then its next most profitable product, and so on.

In order to draw the graph, it is therefore necessary to work out the C/S ratio of each product being sold before ranking the products in order of profitability. It is easy here for Company A, since only two products are being produced, and so it is useful to draw a quick table as see on the spreadsheet below (prevents mistakes in the exam hall) in order to ascertain each of the points that need to be plotted on the graph in order to show the profit/loss lines.

The table should show the cumulative revenue, the contribution earned from each product and the cumulative profit/(loss). It is the cumulative figures which are needed to draw the graph.

The graph can then be drawn ( Figure 3 ), showing cumulative sales on the x axis and cumulative profit/loss on the y axis. It can be observed from the graph that, when the company sells its most profitable product first (X) it breaks even earlier than when it sells products in a constant mix. The break-even point is the point where each line cuts the x axis.

Limitations of cost-volume profit analysis

• Cost-volume-profit analysis is invaluable in demonstrating the effect on an organisation that changes in volume (in particular), costs and selling prices, have on profit. However, its use is limited because it is based on the following assumptions: Either a single product is being sold or, if there are multiple products, these are sold in a constant mix. We have considered this above in Figure 3 and seen that if the constant mix assumption changes, so does the break-even point.
• All other variables, apart from volume, remain constant – ie volume is the only factor that causes revenues and costs to change. In reality, this assumption may not hold true as, for example, economies of scale may be achieved as volumes increase. Similarly, if there is a change in sales mix, revenues will change. Furthermore, it is often found that if sales volumes are to increase, sales price must fall. These are only a few reasons why the assumption may not hold true; there are many others.
• The total cost and total revenue functions are linear. This is only likely to hold a short-run, restricted level of activity.
• Costs can be divided into a component that is fixed and a component that is variable. In reality, some costs may be semi-fixed, such as telephone charges, whereby there may be a fixed monthly rental charge and a variable charge for calls made.
• Fixed costs remain constant over the 'relevant range' - levels in activity in which the business has experience and can therefore perform a degree of accurate analysis. It will either have operated at those activity levels before or studied them carefully so that it can, for example, make accurate predictions of fixed costs in that range.
• Profits are calculated on a variable cost basis or, if absorption costing is used, it is assumed that production volumes are equal to sales volumes.

Written by a member of the Performance Management examining team

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Cost-Volume-Profit (CVP) Analysis- Explained With Examples

Cost-Volume-Profit (CVP) analysis is a management accounting technique that is used to determine the relationship between the cost of producing a product, the volume of sales, and the resulting profits.

CVP analysis helps businesses understand the financial impact of different decisions and to make informed decisions that maximize profits.

CVP analysis involves the use of several key concepts, including:

• Fixed costs : These are costs that remain constant regardless of the volume of sales, such as rent and salaries.
• Variable costs : These are costs that vary depending on the volume of sales, such as raw materials and labor.
• Sales price : This is the price at which a product is sold.
• Break-even point : This is the point at which the company’s total revenues are equal to its total costs. At this point, the company is neither making a profit nor incurring a loss.
• Contribution margin : This is the difference between the sales price and the variable cost per unit. It represents the amount of revenue that contributes to covering the fixed costs and generating a profit.

To illustrate the concept of CVP analysis, let’s consider the example of a company that produces and sells widgets.

The company has fixed costs of $10,000 per month, variable costs of $5 per widget, and sells widgets for $10 each.

Using CVP analysis, we can calculate the break-even point for the company as follows:

Break-even point = Fixed costs / (Sales price – Variable costs per unit) Break-even point = $10,000 / ($10 – $5) Break-even point = 2,000 units

This means that the company needs to sell 2,000 widgets to cover its fixed costs and break even. If the company sells less than 2,000 widgets, it will incur a loss; if it sells more than 2,000 widgets, it will profit.

We can also use CVP analysis to calculate the contribution margin per unit and the total contribution margin:

Contribution margin per unit = Sales price – Variable cost per unit Contribution margin per unit = $10 – $5 Contribution margin per unit = $5

Total contribution margin = Contribution margin per unit x Number of units sold Total contribution margin = $5 x 3,000 Total contribution margin = $15,000

This means that for every widget sold, the company contributes $5 towards covering the fixed costs and generating a profit. In this example, the total contribution margin for the company is $15,000 for 3,000 units sold.

Identifying Fixed Costs in Cost-Volume-Profit (CVP) Analysis

Fixed costs remain constant regardless of the volume of sales or production. These costs are incurred by a company regardless of whether it produces or sells anything. Examples of fixed costs include rent, salaries, property taxes, and insurance premiums.

Identifying fixed costs is important for several reasons. First, fixed costs are an important component of CVP analysis, which helps businesses to understand the financial impact of different decisions. Second, fixed costs can significantly impact a company’s profitability and cash flow . Finally, fixed costs are important for budgeting and forecasting.

To illustrate the concept of identifying fixed costs, let’s consider the example of a retail store. The store has fixed costs of $10,000 per month, which includes rent, salaries, and other fixed expenses. Regardless of the store’s sales volume, the fixed costs remain constant.

If the store sells $20,000 worth of merchandise in a month, the variable costs, such as the cost of goods sold, maybe $10,000. The contribution margin, which is the difference between the sales revenue and the variable costs, would be $10,000.

The contribution margin can be used to cover the fixed costs and generate a profit. In this example, the contribution margin of $10,000 can be used to cover the fixed costs of $10,000 and generates zero profit.

If the store sells $30,000 worth of merchandise monthly, the variable costs may increase to $15,000. The contribution margin would be $15,000, which is higher than the fixed costs of $10,000. This would result in a profit of $5,000 for the month.

If the store sells $10,000 worth of merchandise in a month, the contribution margin would be zero, and it could not cover its fixed costs. This would result in a loss of $10,000 for the month.

In this example, identifying fixed costs is essential for understanding the store’s profitability and cash flow. The store can make informed decisions about pricing, product mix, and resource allocation by understanding the fixed costs . The store can also use fixed costs for budgeting and forecasting to ensure that it can cover its expenses and generate a profit.

In summary, fixed costs are costs that remain constant regardless of the volume of sales or production. Identifying fixed costs is important for understanding a company’s profitability and cash flow, making informed decisions, and budgeting and forecasting.

Identifying Variable Costs in Cost-Volume-Profit (CVP) Analysis

Variable costs are costs that vary with the level of production or sales. These costs increase or decrease as production levels or sales volumes change. Examples of variable costs include direct materials, direct labor, and variable manufacturing overhead.

Understanding variable costs is essential for conducting Cost-Volume-Profit (CVP) analysis. CVP analysis helps businesses to understand the financial impact of different decisions, such as changes in sales volume, selling prices, or costs. Businesses can calculate their contribution margin by analyzing variable costs and determining their break-even point.

To illustrate the concept of variable costs in CVP analysis, let’s consider the example of a company that produces and sells widgets. The company has a selling price of $10 per widget, and its variable costs are $5 per widget. This means that the company incurs $5 in variable costs for every widget sold.

Using CVP analysis, we can calculate the company’s contribution margin, which is the amount of revenue left over after variable costs have been deducted. The contribution margin is calculated as follows:

Contribution margin = Selling price – Variable cost per unit Contribution margin = $10 – $5 Contribution margin = $5

This means that for every widget sold, the company has a contribution margin of $5. The contribution margin can be used to cover the company’s fixed costs and generate a profit.

We can also use CVP analysis to determine the company’s break-even point, which is the point at which its total revenues are equal to its total costs. The break-even point is calculated as follows:

Break-even point = Fixed costs / Contribution margin per unit Break-even point = $10,000 / $5 Break-even point = 2,000 units

By analyzing variable costs in CVP analysis, businesses can make informed decisions about pricing, product mix, and resource allocation. For example, the company could use CVP analysis to determine the impact of a price increase on its profits or to decide whether to produce and sell a new product line . Understanding variable costs is essential for conducting CVP analysis and for making informed decisions that maximize profits.

Identifying Sales Price in Cost-Volume-Profit (CVP) Analysis

The sales price is the amount of money that a company charges for its products or services. In Cost-Volume-Profit (CVP) analysis, the sales price is an important component used to calculate contribution margin, break-even point, and profitability.

Understanding the impact of changes in sales price is critical for businesses to make informed decisions that maximize profits. By analyzing the impact of different sales prices on contribution margin and profitability, businesses can determine the optimal price point for their products or services.

To illustrate the concept of the sales price in CVP analysis, let’s consider the example of a company that produces and sells widgets. The company has a fixed cost of $10,000 per month, and its variable cost is $5 per widget. The company sells widgets for $10 each.

Contribution margin = Sales price – Variable cost per unit Contribution margin = $10 – $5 Contribution margin = $5

This means that the company needs to sell 2,000 widgets to cover its fixed costs and break even.

If the company were to increase the sales price of its widgets to $12, the contribution margin would increase to $7 per widget. This means that for every widget sold, the company would have a contribution margin of $7, which is $2 higher than its current contribution margin of $5.

Using the new sales price of $12, we can recalculate the break-even point as follows:

Break-even point = Fixed costs / Contribution margin per unit Break-even point = $10,000 / $7 Break-even point = 1,429 units

This means that the company needs to sell 1,429 widgets to cover its fixed costs and break even. By increasing the sales price of its widgets, the company has reduced its break-even point and can generate a profit with fewer units sold.

In summary, the sales price is an important component of Cost-Volume-Profit (CVP) analysis. By understanding the impact of changes in sales price on contribution margin, break-even point, and profitability, businesses can make informed decisions about pricing that maximize profits .

Identifying Break Even Point in Cost-Volume-Profit (CVP) Analysis

The break-even point is a key concept in Cost-Volume-Profit (CVP) analysis. It represents the level of sales at which a company’s total revenues are equal to its total costs, resulting in neither a profit nor a loss.

The break-even point is important because it gives businesses a clear understanding of the sales volume they need to achieve to cover their costs and profit. It can also help businesses to make informed decisions about pricing, product mix, and resource allocation.

To illustrate the concept of the break-even point in CVP analysis, let’s consider the example of a company that produces and sells widgets. The company has fixed costs of $10,000 per month, and its variable cost is $5 per widget. The company sells widgets for $10 each.

We can use the contribution margin to calculate the company’s break-even point, which is the level of sales at which its total revenues are equal to its total costs. The break-even point is calculated as follows:

Businesses can use the break-even point to make informed decisions about pricing, product mix, and resource allocation. For example, the company could use the break-even point to determine the minimum sales volume needed to launch a new product line or to decide whether to invest in new equipment to increase production capacity.

In summary, the break-even point is the level of sales at which a company’s total revenues are equal to its total costs, resulting in neither a profit nor a loss. It is an important concept in Cost-Volume-Profit (CVP) analysis and can help businesses to make informed decisions about pricing, product mix, and resource allocation.

Identifying Contribution Margin Point in Cost-Volume-Profit (CVP) Analysis

The contribution margin is a key concept in Cost-Volume-Profit (CVP) analysis. It helps businesses understand how much each product unit contributes to covering their fixed costs and generating a profit.

In simple terms, the contribution margin is the difference between the sales price of a product and the variable costs associated with producing that product. The contribution margin covers the business’s fixed costs and generates a profit.

To illustrate the concept of contribution margin in CVP analysis, let’s consider the example of a company that produces and sells widgets. The company has a selling price of $10 per widget, and its variable costs are $5 per widget. This means that the company incurs $5 in variable costs for every widget sold.

The contribution margin can also be expressed as a percentage of the sales price. In the case of our example company, the contribution margin percentage would be:

Contribution margin percentage = Contribution margin / Sales price Contribution margin percentage = $5 / $10 Contribution margin percentage = 50%

This means that 50% of the sales price of each widget is available to cover the company’s fixed costs and generate a profit.

Businesses can use the contribution margin to make informed decisions about pricing, product mix, and resource allocation. For example, the company could use the contribution margin to determine the profitability of a new product line or to analyze the impact of changes in selling prices or variable costs.

In summary, the contribution margin is the amount of revenue left over after variable costs have been deducted from the sales price of a product. It is an important concept in Cost-Volume-Profit (CVP) analysis and can help businesses make informed decisions about pricing, product mix, and resource allocation.

How Does Cost-Volume-Profit (CVP) Analysis Help Manufacturers?

CVP analysis can be used to make informed decisions about pricing, product mix, and resource allocation.

For example, the company could use CVP analysis to determine the impact of a price increase on its profits or to decide whether to produce and sell a new product line.

CVP analysis provides valuable insights into a company’s financial performance and helps managers make informed decisions that maximize profits.

Where do cost accountants find information to perform Cost-Volume-Profit (CVP) Analysis

Cost-Volume-Profit (CVP) analysis requires accountants to have access to various types of financial and operational data to perform accurate and reliable analyses. Here are some common sources of information that accountants use to perform CVP analysis:

• Financial statements: Accountants can gather information about sales revenue, variable costs, and fixed costs from the company’s income statement and balance sheet .
• Sales data: Accountants can obtain detailed sales volume and pricing information from sales reports or the company’s customer relationship management (CRM) system.
• Cost data : Accountants can obtain information about variable and fixed costs from the company’s accounting system, including detailed cost reports and general ledger transactions.
• Production data: Accountants can obtain information about the number of units produced and sold from the company’s manufacturing or operations system.
• Market research: Accountants can gather information about industry trends, competitor pricing, and customer demand from market research reports or online sources.

By gathering and analyzing this information, accountants can perform CVP analysis and make informed decisions about pricing, product mix, and resource allocation. Accountants need to ensure the accuracy and reliability of the data they use in their analyses to ensure that their conclusions are sound and reliable.

What are the typical watch outs when performing Cost-Volume-Profit (CVP) Analysis?

There are several watch-outs that accountants should keep in mind when performing Cost-Volume-Profit (CVP) analysis to ensure that their analyses are accurate and reliable. Some of these watch outs include:

• Assumptions : CVP analysis involves making assumptions about the behavior of costs and revenues, such as assuming that fixed costs remain constant over a certain period of time. Accountants need to ensure that these assumptions are valid and based on realistic expectations.
• Cost behavior : Accountants should clearly understand how costs behave in relation to changes in sales volume. For example, they should understand whether a cost is fixed or variable and how it will change with changes in sales volume.
• Sales mix : If a company sells multiple products with different sales prices and variable costs, it is important to consider the sales mix when performing CVP analysis. Accountants should ensure that their analysis accurately reflects the proportion of each product sold.
• Time period : CVP analysis typically assumes that costs and revenues remain constant over a certain period of time. Accountants should ensure that the time period used in their analysis is appropriate and reflects the business’s operations.
• Accuracy of data : CVP analysis relies on accurate and reliable data. Accountants should ensure that the data used in their analysis is accurate and that any assumptions or estimates used are based on realistic expectations.
• Margin of safety : It is important to consider the margin of safety when performing CVP analysis. This is the amount by which actual sales exceed the break-even point. Accountants should ensure that the margin of safety is sufficient to cover unexpected changes in costs or sales volume.

By keeping these watch-outs in mind, accountants can perform accurate and reliable CVP analysis and make informed decisions about pricing, product mix, and resource allocation.

Cost-Volume-Profit (CVP) Analysis- Conclusion

In conclusion, Cost-Volume-Profit (CVP) Analysis is essential for businesses to understand their profit structure and make informed decisions to maximize profits.

By analyzing the relationship between the cost of production, sales revenue, and overall profit, businesses can determine the break-even point and the required sales volume to achieve a desired profit level.

Moreover, CVP analysis can help businesses determine the most profitable mix of products and the most effective sales strategies. It is important for businesses to regularly conduct CVP analysis and adjust their strategies accordingly to stay competitive and maximize profits.

Ultimately, CVP analysis provides a clear picture of a business’s financial situation and allows for strategic planning to achieve long-term success.

Cost-Volume-Profit (CVP) Analysis- Recommended Reading

• Your Accountants Are Lying to You: 4 Ways Describing How
• Product Profitability Analysis: Definition, How to Do, and Examples
• Process Costing: Definition, Types, Importance, Advantages and Disadvantages

Updated: 5/18/2023

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Cost-Volume-Profit Analysis: CVP Formula and Examples

by Maria Del | Mar 13, 2024

Cost volume profit analysis is a financial planning tool frequently used to assess the viability of short-term strategies. Among other things, break-even and what-if analyses are carried out for a variety of scenarios to estimate the effects on profits of short-term changes in cost, volume, and selling price.

In this article, you will learn about CVP analysis and its components, as well as the assumptions and limitations of this method. Additionally, you will learn how to carry out this type of analysis in Google Sheets, so you can easily repeat it periodically. Using Layer, you can seamlessly connect your data across multiple locations and formats, and the whole team will have access to updated information.

What is a Cost Volume Profit Analysis?

Cost Volume Profit (CVP) analysis is used in cost accounting to determine how a company’s profits are affected by changes in sales volume, fixed costs, and variable costs. Various techniques are involved, including the calculation of the contribution margin and the contribution margin ratio, the break-even point, the margin of safety, and what-if analysis.

Why is a Cost Volume Profit Analysis Important?

Cost volume profit analysis can be used to justify embarking on manufacturing a new product or providing a new service. By analyzing fixed and variable costs separately, CVP analysis provides insight into the profitability of different products and services, allowing you to make smarter decisions.

You can analyze different scenarios to determine how much you would need to sell in order to break even or reach a certain profit margin. You can also calculate your margin of safety to determine how far your sales can drop and you still break even.

How To Perform A Cost Volume Profit Analysis?

There are three main components to CVP analysis: cost, sales volume, and price. There are also multiple techniques involved in CVP analysis, allowing you to evaluate as many or as few scenarios as you need. Generally speaking, the CVP formula is the following: profit = revenue – costs.

1. Contribution Margin and Ratio

The contribution margin ratio and the variable expense ratio can help you evaluate your company’s profitability with respect to variable expenses. The contribution margin can be calculated to get a total dollar amount or an amount per unit. To get a total dollar amount, subtract the total variable costs from the total sales amount.

Contribution margin = Total sales amount – Total variable costs

The contribution margin per unit is calculated by subtracting the variable cost per unit from the selling price per unit.

Contribution margin = Unit selling price – Unit variable costs

To obtain the contribution margin ratio, simply divide by total sales and selling price, respectively.

2. Break-Even Point

The break-even point (BEP) refers to the moment when you neither lose nor make money: your profits equal your losses. This tells you how much you need to sell to ensure your profits cover your costs. The break-even point can be calculated in units or in dollars. To learn more about break-even analysis and how to calculate the break-even point, check out our article on  Break-Even Analysis .

3. Margin of Safety

The margin of safety shows you how much your sales can drop while still allowing your company to break even. To find the margin of safety, simply subtract the break-even amount for sales from the actual sales for your company.

Margin of safety = Actual sales amount – Break-even sales amount

You can express this as a percentage by dividing it by the actual sales amount.

4. What-If Analysis

You can evaluate different strategies using what-if analysis and setting a profit target. This will allow you to estimate how this affects the other variables involved, such as sales price or quantity produced. To learn about what-if analysis, as well as how to do it in Google Sheets, check out our related article on  How To Perform What-If Analysis in Google Sheets .

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Cost Volume Profit Analysis Assumptions

When carrying out CVP analysis, it’s important to remember that it makes certain key assumptions that don’t necessarily reflect reality, at least in the long term.

For example, both the fixed cost per unit and the variable cost per unit are considered to be constant, and so is the sales price. While this may or may not be true in the short term, it’s very unlikely to remain true for longer timespans. For this reason, this analysis is more effective when evaluating short-term decisions.

Example of Cost Volume Profit Analysis

Below, you have step-by-step instructions on how to perform CVP analysis in Google Sheets.

Step 1: Set Up Data

In Google Sheets, set up the data you need for the CVP analysis: total sales and selling price, total variable and fixed costs, as well as variable and fixed costs per unit.

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Step 3: Calculate Break-Even Point

You can calculate the break-even point in units or in dollars.

1.  Divide the fixed costs by the contribution margin per unit.

Step 4: Calculate the Margin of Safety

Finally, you can calculate the margin of safety – in dollars or as a percentage of sales – to calculate how much sales could drop while still breaking even.

1.  Subtract the break-even amount from the sales amount.

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What Is Cost-Volume-Profit (CVP) Analysis?

• Understanding CVP Analysis

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Cost-Volume-Profit (CVP) Analysis: What It Is and the Formula for Calculating It

Katrina Ávila Munichiello is an experienced editor, writer, fact-checker, and proofreader with more than fourteen years of experience working with print and online publications.

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• Cost-Volume-Profit (CVP) Analysis CURRENT ARTICLE
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Cost-volume-profit (CVP) analysis is a method of evaluating the impact that varying levels of costs and volume have on a company's operating profit.

Key Takeaways

• Cost-volume-profit (CVP) analysis is used to find out how changes in variable and fixed costs impact a firm's profit.
• Companies can use CVP analysis to see how many units they need to sell to break even (cover all costs) or, alternatively, how many units they need to sell to reach a certain minimum profit margin.
• CVP analysis can also be used to calculate the contribution margin of a firm's products; the contribution margin is the difference between total sales and total variable costs.
• For a business to be profitable, its contribution margin must exceed its total fixed costs of production.

Investopedia / Daniel Fishel

Understanding Cost-Volume-Profit (CVP) Analysis

Cost-volume-profit (CVP) analysis, also referred to as breakeven analysis, can be used to determine the  breakeven point for different sales volumes and cost structures. The breakeven point is the number of units that need to be sold—or the amount of sales revenue that has to be generated—to cover the costs required to make the product.

CVP analysis can be useful for companies when making short-term business decisions. Running a CVP analysis involves using several equations for price, cost, and other variables; these equations are plotted on a graph.

Cost-Volume-Profit (CVP) Analysis Formula

One key CVP formula is the formula used to calculate a company's breakeven point. The breakeven sales volume formula is:

Breakeven Sales Volume = F C C M where: F C = Fixed costs C M = Contribution margin = Sales − Variable Costs \begin{aligned} &\text{Breakeven Sales Volume}=\frac{FC}{CM} \\ &\textbf{where:}\\ &FC=\text{Fixed costs}\\ &CM=\text{Contribution margin} = \text{Sales} - \text{Variable Costs}\\ \end{aligned} ​ Breakeven Sales Volume = CM FC ​ where: FC = Fixed costs CM = Contribution margin = Sales − Variable Costs ​

For example, a company with $100,000 of fixed costs and a contribution margin of 40% must earn revenue of $250,000 to break even.

In addition to calculating the breakeven point, the formula above can also be tweaked to determine a company's target sales volume (in order to achieve its target profit): Add a target profit amount per unit to the fixed-cost variable of the formula.

For example, if the previous company desired a profit of $50,000, the necessary total sales revenue is found by dividing $150,000 (the sum of fixed costs and desired profit) by the contribution margin of 40%. This example yields a required sales revenue of $375,000.

Cost-Volume-Profit (CVP) Analysis and Contribution Margin

CVP analysis can also be used to calculate the contribution margin. The contribution margin is the difference between total sales and total variable costs. For a business to be profitable, the contribution margin must exceed total fixed costs.

The contribution margin may also be calculated per unit (per product). The unit contribution margin is simply the remainder after the unit variable cost is subtracted from the unit sales price.

The contribution margin ratio is determined by dividing the contribution margin by total sales.

The contribution margin is part of the formula used to determine the breakeven point of sales. By dividing the total fixed costs by the contribution margin ratio, the breakeven point of sales—in terms of total dollars—may be calculated.

CVP analysis is only reliable if costs are fixed within a specified production level. All units produced are assumed to be sold, and all fixed costs must be stable in CVP analysis. Another assumption is all changes in expenses occur because of changes in activity level. Semi-variable expenses must be split between expense classifications using the high-low method , scatter plot, or statistical regression.

How Is Cost-Volume-Profit (CVP) Analysis Used?

CVP analysis is used to determine whether there is an economic justification for a product to be manufactured. A target profit margin is added to the breakeven sales volume, which is the number of units that need to be sold in order to cover the costs required to make the product (and arrive at the target sales volume needed to generate the desired profit). The decision maker could then compare the product's sales projections to the target sales volume to see if it is worth manufacturing.

What Assumptions Does Cost-Volume-Profit (CVP) Analysis Make?

The reliability of CVP lies in the assumptions it makes, including that the sales price and the fixed and variable cost per unit are constant. The costs are fixed within a specified production level. All units produced are assumed to be sold, and all fixed costs must be stable. Another assumption is all changes in expenses occur because of changes in activity level. Semi-variable expenses must be split between expense classifications using the high-low method, scatter plot , or statistical regression.

What Is Contribution Margin?

The contribution margin can be stated on a gross or per-unit basis. It represents the incremental money generated for each product/unit sold after deducting the variable portion of the firm's costs. Basically, it shows the portion of sales that helps to cover the company's fixed costs. Any remaining revenue left after covering fixed costs is the profit generated. So, for a business to be profitable, the contribution margin must exceed total fixed costs.

Cost-volume-profit (CVP) analysis is a method of evaluating how changes in costs and volume impact a business' operating profit. CVP analysis is often used to determine the breakeven point: the number of units that need to be sold—or the amount of sales revenue that has to be generated—to cover the costs required to make a given product.

CVP analysis can also be used to calculate the contribution margin of a firm's products; for a business to be profitable, its contribution margin must exceed its total fixed costs of production. The contribution margin can be calculated by subtracting the total variable costs of production from total sales.

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A STUDY ON COST VOLUME PROFIT ANALYSIS AT GASHA STEELS PVT LTD., KANJIKODE PROJECT REPORT

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An excel add-in to help you save time and enhance your modeling and analysis., cost-volume-profit analysis and break-even point, dobromir dikov.

Today we will take a look at Cost-Volume-Profit (CVP) analysis and the Break-even point (BEP) in sales.

Cost-Volume-Profit Analysis

The Cost-Volume-Profit  (CVP) analysis is a method of cost accounting. It looks at the impact of changes in production costs and sales on operating profits. Performing the CVP, we calculate the Break-even point for various sales volume and cost structure scenarios, to help management with the short-term decision-making process. As it focuses mainly on the Break-even point, it is commonly referred to as Break-even Analysis.

When performing a CVP analysis, we need to consider the following inherent assumptions:

• Selling price is constant for varying quantities of sold units;
• Fixed Costs are consistent at the specified production levels;
• Variable Costs per unit do not vary between different numbers of produced units;
• All manufactured items are sold in the same period;
• Costs are classified as Fixed or Variable; no semi-fixed costs can exist in the analysis;
• All costs are only affected by changes in the activity.

The CVP formula shows us the sales volume needed to cover costs and break even. The recipe for the break-even sales is:

We know where Fixed Costs come from, now let us look at the contribution margin.

Contribution margin

To calculate the CVP equation, we first take a look at the Contribution Margin.

The Contribution Margin (CM) is a basic calculation in CVP analysis. It represents the profit the company has made, to cover Fixed Costs. We can also calculate it on a per-unit basis. Another calculation is the Contribution Margin ratio:

We can conclude that whenever the Contribution Margin is more than the Fixed Costs, the business is profitable.

Break-even point

The volume of production and sales where all relevant costs are covered by the revenue is called the break-even point (BEP). This is where the business breaks even and can start generating income. The BEP represents the level of sales where net income = zero , the point where Sales = Total Variable Costs + Total Fixed Costs , and Contribution Margin = Total Fixed Costs .

To calculate the break-even amount, we divide the Total Fixed Costs over the Contribution Margin ratio:

Another way to calculate the break-even amount is as follows:

To calculate the quantity of the break-even point, we use the following formula:

Another way to calculate the break-even point in units is to look at the break-even equation:

By solving the equation for Q , we can find the break-even point in volume of units.

Targeted income

We can also calculate the CVP equation to get the required sales volume to realize the desired target profit (targeted income).

We add the target income to the Fixed Costs:

If we are calculating the break-even sales for the whole company, and not for a division, we can then also add the income tax we have to cover with sales, to arrive at the targeted income. Then we will adjust the formula as follows:

CVP Graph and example

We can also graphically present the CVP analysis. Let us look at an example to create a CVP analysis Graph.

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Let us start with the following data:

• Total Fixed Costs are 100,000 euros;
• Variable Costs per unit are 2,20 euros;
• Selling Price per unit is 4,00 euros.

Using those we can calculate the Total Costs (Variable and Fixed) and Sales Revenue for different volume levels:

We can then calculate the Break-even point using the formulas we discussed above.

Contribution Margin per Unit = Selling Price – Variable Costs per unit = 4.00 – 2.20 = 1.80 euros per unit

The Break-even volume is = Total FC / CM per Unit = 100,000 / 1.80 = 55,556 units

The corresponding break-even sales will be the break-even volume multiplied by the selling price of 4.00 euros, or:

55,556 * 4.00 = 222,222 euros .

To plot this in Excel we use an XY Scatter data series on top of our Line series, and we also present it proportionally from the number of XY Scatter data points (look at the Excel file available for download at the end of the article).

We then get the following chart or CVP Graph:

The graphical representation of the CVP analysis shows us the following:

• The blue line shows our sales, increasing as the volume increases, multiplied by the selling price of 4.00 euros;
• The brown line shows fixed costs, which are not affected by sales volume and remain constant;
• The grey line shows our variable costs, at 2.20 euro per unit;
• The yellow line shows total costs (fixed costs + variable costs) for the respective sales volume;
• The break-even point is at the sales volume where sales revenue crosses above the total costs line, which means that we start to generate net income from this point on;
• Based on our calculations, we know that the company will break even when 55,556 units are sold for 222,222 euros.

Contribution margin income statement

Let us look at a more financial representation of the CVP analysis. If we present the calculations in the income statement format, we get the contribution income statement, which is primarily used for internal purposes in companies. By calculating the break-even volume with a targeted pre-tax income of 45,000 euros, we get 80,556 units. Calculating sales and variable costs for this quantity, we get the following:

Looking at CVP this way we get a more comprehensive view of required sales volumes to get a 45,000 euros pre-tax income. This income statement shows us that to get the targeted income; we have to achieve the respective sales and keep variable and fixed costs at the specified levels.

Benefits and Limitations of CVP

The CVP analysis is easy to implement financial analysis technique that can help us with decision making for production volumes. However, we must consider the following benefits and limitations that it faces:

• (+) CVP provides a simple understanding of the sales required to break even or achieve a desired profitability;
• (+) It helps decision-makers with forecasting cost and profit based on activity changes;
• (+) CVP also helps management decide on the optimum levels of production, to maximize profits;
• (-) CVP assumes the scale of production doesn’t affect Total Fixed Costs, which is rarely the case in real-life scenarios;
• (-) Variable Costs are expected to vary proportionally with production/sales volume, which doesn’t happen in reality;
• (-) CVP assumes costs are either Fixed or Variable when in fact a lot of costs are semi-fixed, and their separation to fixed and variable components may not always be achievable.

The Cost-Volume-Profit analysis is a short-run marginal analysis method that can help us with decision making in regards to optimum production and sales volumes. However, we must keep in mind the assumptions that it makes, which can be hard to set correctly. If the reality deviates too much from the initial assumptions, we might get a CVP analysis that provides us with conclusions that are not very beneficial for the company.

This was a brief view of Cost-Volume-Profit analysis and Break-even point  in sales. To review the example calculations, download the attached Excel working file below:

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Mend: A Case in Cost-Volume-Profit Analysis Harvard Case Solution & Analysis

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Mend: A Case in Cost-Volume-Profit Analysis Case Solution

A brief instance emphasize the usages and constraints for cost-volume -profit evaluation.

published: 07 Mar 2013

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