This lesson introduces cost-volume-profit analysis. 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:
The first two items are information available to business managers, about their own business, products and services. This type of information is not generally available to those outside the business. They constitute important operating information that can help managers assess past performance, plan for the future, and monitor current progress. As for the third item, a business can’t stay in business very long without
profits.
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.
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.
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.
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
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.
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 lesson we will ignore both inventory changes and income taxes. Here, you should gain a basic working knowledge of CVP Analysis fundamentals.
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:
Parts prices vary over time. Currently the cost to produce one bicycle is $70.
| 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:
Total Fixed Costs (FC) do not change as production/sales increases. Unit Fixed Costs decrease as production increases within the relevant range.
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:
EXAMPLE: Mike’s Bikes spends $5,000 per month in fixed costs.
| If they make X bicycles per month…. | their fixed costs PER UNIT will be…… |
| 1,000 bicycles | $5,000 / 1,000 bicycles = $5.00 per bicycle |
| 2,000 bicycles | $5,000 / 2,000 bicycles = $2.50 per bicycle |
| 3,000 bicycles | $5,000 / 3,000 bicycles = $1.67 per bicycle |
| 4,000 bicycles | Try these on your own! |
| 5,000 bicycles | Scroll down for the answers. |
Do Total Fixed Costs change as production goes up?
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.
Quiz Answers
$5,000 / 4,000 bicycles = $1.25 per bicycle
$5,000 / 5,000 bicycles = $1.00 per bicycle
Do Total Fixed Costs change as production goes up? No. Total Fixed Costs stay the same as production goes up. Unit Fixed Costs decrease as productions goes up.
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:
| Fixed component | $20.00 |
| Variable component | $10.00 (100 extra miles @ $ .10) |
| Total cost | $30.00 |
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 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.
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.
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.
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
2) Calculate BE units
| BE Units | = | Total Fixed Costs Unit CM | = | 2000 20 | = | 100 units to break even |
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?
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.
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.
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.