Chapter 20
Cost-Volume-Profit Analysis

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CVP Analysis is a way to quickly answer a number of important questions about the profitability of a company's products or services. CVP Analysis can be used with either a product or service. Our examples will usually involve businesses that produce products, since they are often more complex situations. Service businesses (health care, accounting, barbers & beauty shops, auto repair, etc.) can also use CVP Analysis. 

It involves three elements:

1. Cost - the cost of making the product or providing a service
2. Volume - the number of units of products produced or hours/units of service delivered
3. Profit - Selling Price of product/service - Cost to make product/provide service = Operating Profit

It is important to know whether the company is profitable as a whole. It is also important to know if a particular product is profitable. A business that sells 100 or more different products may lose sight of a single product. If that product becomes unprofitable (selling for less than the cost to produce & sell), the company will lose money on each and every sale of that product. The company might raise the selling price, cut production costs or discontinue the product entirely. Building a business with 100 products we know are profitable is good management. CVP & variable costing provide the tools to make this happen in a real business.

A successful business can be built around a single profitable product. It can also be built around hundreds or thousands of profitable products. Many businesses start small and grow over time, adding products as they gain experience and are able to identify and/or develop new markets and products. No matter the size of the business or the number of products, the same rules apply. Each product must "carry its own weight" for the business to be profitable.

Using CVP Analysis we can analyze a single product, a group of products, or evaluate the entire business as a whole. The ability to work across the entire product line in this way gives us a powerful tool to analyze financial information. It provides us with day-to-day techniques that are easy to understand and easy to use. The concepts parallel the real world, so they are easy to visualize and use. The math is very simple - no complex formulae or techniques. Just simple formulae that can be easily modified to analyze a large variety of situations.

Quiz Yourself
CVP Analysis is important because:
a. the teacher says so.
b. it sounds cool to say "see vee pee". 
c. it is a good way to analyze the profitability of a company's products or services.
d. I haven't a clue.

Click for answer

CVP Relationships
Cost - product cost, consisting of materials, labor, overhead, etc.
Volume - number of units of product sold in a given period of time
Profit - Selling Price minus Cost, per unit or in total

The greater the volume, the greater the TOTAL profit.
 

Approaches to product costs 
Full Costing is used in financial accounting. The full cost of a product includes materials, labor and manufacturing overhead. Not included: Selling and administrative costs.

Variable Costing is used in managerial accounting. Costs are classified as either Variable or Fixed, depending on their Cost Behavior.
 

Cost Behavior
Costs are classified according to how they behave, in relation to units of production. 

CAUTION: Cost behavior can be viewed in terms of total costs or unit costs. Both approaches will be used, but they are not interchangeable. 
 

Fixed Costs
Total Fixed Costs - stay essentially the same month to month, regardless of the number of units produced.

Unit Fixed Costs - goes down as production goes up
 

Variable Costs
Total Variable Costs - go up and down in direct proportion to units produced.

Unit Variable Costs - stay the same regardless of how many units are produced.

Accounting information is captured once by the accounting system. In Accounting I you learned how to analyze transactions, record journal entries, post to the ledger accounts and prepare financial statements for use by those outside the company. That is one way to organize accounting information, but it is not the only way. That same information can be organized in many different ways. In this section we are going to simplify the process greatly. Our topic is Cost-Volume-Profit, so we will focus on income statement accounts, Revenues and Expenses. For now we can ignore balance sheet accounts. 

Managers focus on income statement accounts because these are the ones affected by day-to-day operating activities. Companies produce/purchase and sell products or services. Companies may uses hundreds of income statement accounts to track all their different types of revenues and expenses. We are going to simplify the income statement by dividing all expenses into one of two categories: Variable and Fixed. To master this material you need to master these two concepts.

VARIABLE COSTING - in general
CVP Analysis uses Variable Costing concepts. In this context we will divide ALL costs into one of two categories: Variable or Fixed. We refer to this as "cost behavior." In CVP Analysis cost behavior will be discussed on BOTH a total cost and per unit basis. The facts will remain the same, but the behavior will appear different, depending on the context. Read carefully, especially on exams and in problems, so you understand the context of the question/problem: total cost or per unit. Since CVP Analysis can answer questions about both, we will switch back and forth frequently in our discussion. Tighten you "thinking bolts" and read carefully in this section.

In CVP Analysis we assume that the number of units produced equals the number of units sold. In other words, we factor out changes in inventory during a production period. In the "real world" managers often include inventory changes & income taxes in CVP Analysis. In this course we will ignore both inventory changes and income taxes. Here, you should gain a basic working knowledge of CVP Analysis fundamentals.

VARIABLE COSTS (VC)
Total Variable Costs increase in direct proportion to production/sales.
Unit Variable Costs stay the same as production fluctuates within the relevant range.

EXAMPLE: Mike's Bikes builds the X-Racer from its inventory of parts. Each bicycle is made up of the following parts:

• frame (1)
• seat (1)
• handlebars (1)
• wheels (2)
• tires (2)
• gears & shifting system (1)
• brakes & braking system (1)

UNITS of Product : X-Racer	Cost Per Unit	Total Costs
	1 bicycle = $70	1 bicycle @ $70  = $70
	1 bicycle = $70	2 bicycles @ $70 = $140
	1 bicycle = $70	3 bicycles @ $70 = $210

Per Unit costs stay the same; total costs increase in direct proportion to the number of units produced or sold (sales or production volume). The Relevant Range is the number of units that can be produced or sold under normal circumstances. That might vary due to seasonal demand or factory capacity. To go beyond the relevant range would generally require the additional of more equipment, buildings, personnel, etc. and that would cause a change in all costs. We presume that we are working within the relevant range when doing CVP Analysis. This makes the task much easier. It also helps us understand when we will need to address the need to expand our business.

Variable Costs include any total cost that varies in direct proportion to volume. These commonly include:

• component parts, packaging, etc.
• production labor
• sales commissions (percentage or per unit basis)
• other costs allocated on a per unit basis 

Ask yourself this question: Would a cost be zero if production was zero? If the answer is NO, you are looking at a fixed cost. A common example would be rent on a building. The company must pay rent on the building even if it sells no products in a given month! Some other common costs that follow this pattern are:

• managers & executives salaries
• insurance
• advertising
• real estate & property taxes
• security service
• cleaning & maintenance costs
• depreciation expense on buildings, vehicles & equipment

Quick Quiz
Do Total Fixed Costs change as production goes up?  Click for answer

Since Fixed Cost per Unit goes down as sales/production go up, it is always a good idea to sell/produce more units. In the real world, companies try to produce approximately the same number of units they expect to sell in a given period of time. If you think about the computer industry you will see how important this can be. If a computer company manufactures too many units it may have a stock of merchandise that is hard to sell as new computer chips are introduced to the market. It may have to sell its products at a discount or even at a loss to liquidate its inventory. Chapter 8 discusses "Just In Time" (JIT) inventory management, which is used to help reduce inventory costs, by having parts delivered "just in time" to go into production. JIT inventory systems are commonly used in automobile assembly plants. Using JIT reduces a company's risk of carrying a stock of parts that may quickly become obsolete. 

MIXED COSTS
Mixed costs change somewhat in relation to production, but not proportionately like Variable Costs do. Mixed costs generally have a fixed portion and a variable portion. We deal with these costs by separating them into these two parts - so we are back to only 2 types of cost behavior.

A common example of a mixed cost would be a rental car. You might rent a car for a weekend for $20, for up to a total of 200 miles. You will be charged $ .10 for each additional mile you drive. The flat rate of $20 represents the fixed component; the $ .10 per mile represents the variable component. If you drive 300 miles you will pay:
 

We have a couple of simple ways to separate costs into their fixed and variable components. One way is called the High-Low Method. It looks at the highest & lowest costs over a period of several months to come up with a simple formula that can be used to calculate the variable & fixed costs. Separating mixed costs into their parts is an in-exact practice. At best it is an estimate, or approximation, that is only as accurate as the method we use. This is not usually a significant issue, since all costs are eventually included in our equations. However, if mixed costs constitute a percentage of total costs, it is necessary to be as accurate as possible. More sophisticated methods should be used when a higher level of accuracy is needed.

Contribution Margin
The Contribution Margin (CM) is one of the most essential parts of variable costing and managerial accounting. 

CM = Selling Price - Variable Costs

It can be calculated as either unit CM or total CM. 

CM is the profit available to cover fixed costs and provide net income to the owners.
 

Break Even analysis
One of the first uses of variable costing is calculating the break even point. This is the point at which sales exactly equals total costs. It can be expressed as either units or sales dollars. 

Break Even Units (BE units)- the number of units needed to cover fixed costs for a given period of time. 

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BE units example:
XYZ Co. has monthly fixed costs of $2,000. They sell a single product for $30 each. Variable costs are $10 per unit. They sell about 200 units per month. Calculate the break even point in units.

1) Calculate CM
 

Selling price	$ 30
Variable costs	10
Contribution margin (CM)	$ 20

2) Calculate BE units
 

BE Units

=

Total Fixed Costs Unit CM

=

2000 20

=

100 units to break even

proof:

Contribution margin 100 units @ $20	$ 2000
less Total Fixed Costs	2000
Profit (loss)	$ 0

When sales are below the Break Even point a company is operating at a loss; Above the BE point they will be operating at a profit. The company is selling 200 units per month, well above the break even point, so they are operating at a profit. 

How much profit will they make by selling 200 units per month?
 

Contribution margin 200 units @ $20	$ 4000
less Total Fixed Costs	2000
Profit at 200 units per month	$ 2000

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Example 2:
XYZ is facing fierce competition from a new company, and management decides to lower the selling price of their product to $20 per unit. They also decide to take out advertising at a cost of $400 per month. Recalculate their Break Even point given the new information:

1) Calculate CM 
 

Selling price	$ 20
Variable costs	10
Contribution margin	$ 10

2) Calculate BE units
The $400 advertising costs will increase total fixed costs; add it to the numerator (top number).
 

BE Units

=

Total Fixed Costs Unit CM

=

2400 10

=

240 units at break even

This will be a problem for the company. Their new break even point is higher than their normal monthly sales. They will be operating at a loss under these conditions, and must re-evaluate the decision. 
 

proof:

Contribution margin 200 units @ $10	$ 2000
less Total Fixed Costs	2400
Profit (loss)	($  600)

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Example 3:
We can work the formula in reverse. Assume they include the advertising costs of $400 per month, and sell 200 units. What selling price will put them at the break even point?
 

CM Unit at BE

=

$2400 200

=

$12 CM

They must reverse the calculation, and add variable costs to CM to arrive at the new selling price.

Contribution margin	$ 12
Variable costs	+ 10
Selling price	$ 22

Proof:

Selling price	$ 22
Variable costs	10
Contribution margin	$ 12

 

BE Units

=

Total Fixed Costs Unit CM

=

2400 12

=

200 units at break even

proof:

Contribution margin 200 units @ $12	$ 2400
less Total Fixed Costs	2400
Profit (loss)	$  0

CM Ratio and BE sales volume
The CM can also be viewed as a percentage or ratio. To calculate the CM ratio, divide CM by the Selling Price (SP). 

ABC Co. has monthly fixed costs of $2,400. They sell a single product for $40 each. Variable costs are $24 per unit. They sell about 250 units per month. Calculate their break even point in sales dollars (also called sales volume).
 

Selling price	$ 40
Variable costs	24
Contribution margin	$ 16

Their CM Ratio is CM/SP = 16/40 = .40 or 40%

(In accounting we usually carry calculations out to 4 decimal places).

Break Even Sales Volume

Total Fixed Costs / CM Ratio = 2400/.40 = $6000 in sales per month

proof:
$6000 / $40 SP per unit = 150 units to break even, or:
 

BE Units

=

2400 16

=

150 units at break even

When do we use CM Ratio and BE sales volume?
We can use these calculations anytime. They are especially useful when the company sells a large number of different products - in other words a large sales mix. Take for example a convenience store. They might sell 200 different items, or more. Each item carries its own selling price, and contribution margin per unit. 

Calculating all those contribution margins would be a huge job. And with a sales mix, the company would have to carefully track each and every product. It is much easier to consider the merchandise as a large group, and use the CM Ratio. 

QuikMart operates a convenience store, and their CM Ratio is approximately 42%.  Their monthly overhead (fixed costs) is $2604. What sales volume is needed to break even?

BE volume = TFC / CM Ratio = $2604 / .42 = $6200 per month in sales volume

It is not necessary for the owner to know exactly how many Snickers bars, Milky Way, cans of Coke etc. will be sold each month. That will depend on the what the customers want to buy. The owner will stock a variety of products. By using CM Ratio we don't need to know each item individually. 

Of course, in the real world not all products will earn the same CM Ratio. Some products face stiff competition, and the company will charge accordingly. For instance, they will sell milk at a price similar to grocery stores, earning a rather small CM. But the neat trinkets that adorn the front counter will be sold for twice, three, four times or more their cost, greatly improving the company's overall profit margin. A few high profit items can make up for the "loss leaders" in a company's product mix.

[Loss leaders are products sold at a low price, sometimes at a loss, to attract customers, and get them to shop in your store. Free items, 2-fer sales, 1 cent sales, etc. are all examples of the loss leader strategy used by grocery stores to get your business. They hope you will buy some of the high profit items while you are shopping in their store. Sometimes they will require a minimum purchase, or limit the number of loss leader items a customer can buy.]

CVP Graphs
CVP relationships and the break even formula can all be illustrated with a simple graph. CVP graphs are a great way to convey information. They are especially useful in presenting alternatives to decision makers, many of whom may more easily grasp the concepts with a visual presentation, rather than page full of numbers.