#### Cost Behavior

The contribution margin income statement is a very useful tool in planning and decision making. While it cannot be used for GAAP financial statements, it is often used by managers internally.

The contribution margin income statement is a cost behavior statement. Rather than separating product costs from period costs, like the traditional income statement, this statement separates variable costs from fixed costs.

The basic format of the statement is as follows:

Variable costs, no matter if they are product or period costs appear at the top of the statement. Fixed costs are treated the same way at the bottom of the statement. It is helpful to calculate the variable product cost before starting, especially if you will need to calculate ending inventory.

Let’s run through an example to see how the income statement is constructed. We will use the same figures from the absorption and variable product cost post.

The first thing to remember about any income statement is that the statement is calculated based on the amount of product sold, not the amount of product produced. Therefore, this income statement will be based off the sale of 8,000 units.

To calculate sales, take the price of the product and multiply by the number of units sold.

Sales = Price X Number of units sold

Sales = $100 X 8,000

Sales = $800,000

Next, we need to calculate the variable costs. In the absorption and variable costing post, we calculated the variable product cost per unit.

This covers the product costs, but remember we must include all the variable costs. There is also $5 of variable selling cost that should be included. Multiply the total variable cost per unit by the number of units sold.

Total variable cost = Variable cost per unit X Number of units sold

Total variable cost = ($44 + $5) X 8,000

Total Variable Cost = $392,000

Contribution margin is the amount of sales left over to contribute to fixed cost and profit. Contribution margin can be expressed in a number of different ways, including per unit and as a percentage of sales (called the **contribution margin ratio**). In the contribution margin income statement, we calculate total contribution margin by subtracting variable costs from sales.

Total contribution margin = Sales – Variable costs

Fixed costs include all fixed costs, whether they are product costs (overhead) or period costs (selling and administrative). One thing that causes the contribution margin income statement and variable costing to differ from the traditional income statement and absorption costing is the fact that fixed overhead is treated as if it were a period cost. All fixed overhead is expensed in the period it is incurred. Under absorption costing, fixed overhead is attached to each unit. Therefore if there are units that are not sold, a portion of the fixed overhead ends up in inventory. That is not the case when using variable costing.

Add fixed overhead and fixed selling and administrative to calculate total fixed cost.

Total fixed cost = Fixed overhead + Fixed selling and administrative

Total fixed overhead = $48,000 + $112,000

Total fixed overhead = $160,000

Last step: subtract fixed costs from contribution margin to calculate operating income.

#### Final Thoughts

The contribution margin income statement is all about behavior. Remember the format and ignore the traditional (absorption) income statement. Most students that have trouble with this statement try to relate it back to what is happening on the traditional income statement. Throw out what you know about the traditional income statement when doing the contribution margin income statement. Focus on the format of this statement and you should be fine.

#### Related Video

The contribution margin income statement

In the previous post about mixed cost, we stated that a mixed cost is just the sum of the variable and fixed components. This is fairly easy to deal with when we are dealing with an external cost where we are given the variable rate and the fixed cost. In business, many mixed costs are actually generated internally. Therefore, the variable and fixed components are not clear. We must find a way to calculate the fixed and variable components.

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There are a number of ways to calculate the cost formula for a mixed cost. In this post, we will focus on the high-low method. This method is not the most precise method but it is the easiest to calculate. It does not require spreadsheet or graphing software.

### Why the high-low method works

Below is some data from an oil change service business.

The business has fixed and variable costs but wants an easy way to do cost planning for future budgets. The company would like you to write a mixed cost formula for planning purposes. It might seem daunting at first but it’s really a lot easier than you might think.

#### Step 1 – Find the high point and the low point

Since this is called the high-low method, we first need to determine the highest point and the lowest point in the range. Because the variable rate and fixed costs are not always 100% constant, the cost should not be used. Since the number of oil changes is a consistent, reliable measure, we should use that to determine the high and low points. Looking at the data in the chart above, what would you choose as the high and low points? April is the high point with 2,950 oil changes and January is the low point with 2,200 oil changes.

Once you have picked the high point and the low point, you can throw out the rest of the data. You no longer need it.

#### Step 2 – Find the variable rate

You might be wondering how we are going to jump to solving for the variable rate when it doesn’t seem like we have a whole lot of information. We have more information than you might think.

Let’s look at these two points on a graph.

If you read the post on variable cost or the post on mixed cost, you might remember that we talked about slope. I know that slope is terribly boring and something that you might be trying to forget from your math classes, but is actually important here and makes this concept much easier to understand.

We said in the earlier posts that variable rate is the slope of the line. That means that for every additional oil change performed, the total cost increases by the variable rate. In January (the low point), the company performed 2,200 oil changes with a total cost of $9,860. In April, the company performed 750 more oil changes. Those additional oil changes cost the company an additional $1,725. Over the course of 750 oil changes, cost increased $1,725. That also means that the variable cost of 750 oil changes is $1,725.

Since we know that the variable cost of 750 oil changes is $1,725, we can divide to calculate the variable rate. The variable rate is $2.30.

Let’s go through the calculation step by step so you can see where I got all the numbers.

First calculate the change in cost and the change in activity.

Change in Cost = $11,585 – $9,860 = $1,725

Change in activity = 2,950 – 2,200 = 750

Next we will divide the change in cost by the change in activity to calculate the variable rate.

Variable rate = $1,725 / 750 = $2.30

Most textbooks will use the following formula for variable rate using the high-low method:

If you’ve looked at that formula before and thought “huh?!?”, I agree. Many times in managerial accounting, understanding what is actually happening is much more helpful in solving the problem than trying to memorize the formulas. Just remember that the increase in cost is all variable cost. If you calculate how much the activity changed, you now have the total variable cost for the additional activity. That is enough information to calculate the rate.

#### Step 3 – Find the fixed cost

The formula for mixed cost is:

Total cost = Rate X Activity + Fixed Cost

We need to fill in all the additional information so that we can solve for the fixed cost. We clearly have the rate. We solved for that above.

Total cost = $2.30 X Activity + Fixed Cost

Where could we get figures for total cost and the activity level for that cost? Wouldn’t it be nice if we had some data for total monthly cost and the activity associated with it?

Well, it’s a good thing we have the high and low points. The data gives us exactly what we need. We have the total monthly cost for two of the months and the activity associated with those months. Brilliant!

**Note: You must use the figures from either the high point or the low point since the variable rate was calculated based on those numbers. The high and low points will give you the same fixed cost (within a few cents if you had to round the variable rate).**

Plug either the high point or low point into the cost formula and solve for fixed cost.

$11,585 = $2.30 X 2,950 + Fixed Cost

Fixed Cost = 4,800

OR

$9,860 = $2.30 X 2,200 + Fixed Cost

Fixed Cost = $4,800

#### Step 4 – Write the cost formula

Now that you have the variable rate and the fixed cost, you can write a cost formula for planning. The monthly cost of oil changes is:

Total Monthly Cost = $2.30 X number of oil changes + $4,800

#### Related Video

Mixed Cost and the High-Low Method

As the name suggests, a **mixed cost** is made up of a mix of variable cost and fixed cost. A cost must have both components to be considered a mixed cost.

There are many mixed costs around us. If you look at an electric bill, most will have a fixed customer service charge and various variable charges. We recently rented a moving truck. We were charged a daily rate (fixed cost) plus a rate per mile (variable cost).

The **cost formula** for a mixed cost is the sum of the variable and fixed components.

**Total Mixed Cost = Variable Cost + Fixed Cost**

If you remember the post on variable cost, you’ll remember that the formula for total variable cost is rate x activity. Therefore, we can expand our formula for mixed cost:

**Total Mixed Cost = Rate X Activity + Fixed Cost**

In some books, you will see the mixed cost equation expressed as the slope equation:

**y = mx + b**

y = total mixed cost

m = variable rate

x = activity

b = fixed cost

Don’t let this formula scare you. It’s the same as the formula above it. While it is important to understand that you can graph cost to observe it’s behavior, don’t get overwhelmed by the slope formula. If you understand that a mixed cost has a variable and a fixed component, the formula is pretty easy.

### Calculating a mixed cost

Let’s look at a few examples to see how to calculate a mixed cost.

**Example #1**

**ACI, Inc. is looking to lease a copier. The terms of the agreement state that there will be a monthly lease fee of $99 plus a charge of $0.02 per copy. If ACI plans to make 10,000 copies next month, how much would the copier lease cost?**

First let’s identify the costs in the problem and if they are variable or fixed.

The first cost mentioned is a $99 monthly lease fee. Is this cost fixed or variable? When answering this question, ask yourself if there is a cost driver. Is there any activity that makes the monthly lease fee change? The answer is no. It will be $99 for the term of the lease. Therefore it is fixed.

The other charge is $0.02 per copy. Does this cost have a cost driver? Yes. For every copy that is made, the total cost of copies increases bt $0.02. Therefore this cost is variable.

Since we have identified a variable cost and a fixed cost, the total cost of the copier lease is a mixed cost. Let’s write the cost formula for the cost of the lease.

Total Mixed Cost = Rate X Activity + Fixed Cost

Total Monthly Lease Cost = $0.02 X number of copies + $99

As we do monthly cost planning, we now have a formula to help us plan.

Now answer the question that was asked. Plug the number of copies into the formula and solve.

Total Monthly Lease Cost = $0.02 X 10,000 + $99

Total Lease Cost = $200 + $99

Total Lease Cost = $299

**Example #2**

**ACI, Inc. is doing budget planning for next fiscal year. The company believes that it will make 150,000 copies annually on the copier it plans to lease. What is the total projected cost of the copier for the next fiscal year?**

Let’s go back to our cost equation.

Total Monthly Lease Cost = $0.02 X number of copies + $99

How must we change the formula to use it for annual planning? The current formula is for monthly cost and we are now trying to plan for an annual cost. Take the fixed cost and multiply it by 12.

Total Annual Lease Cost = $0.02 X number of copies + $1,188

Now we can solve.

Total Annual Lease Cost = $0.02 X 150,000 + $1,188

Total Annual Lease Cost = $3,000 + $1,188

Total Annual Lease Cost = $4,188

### Final Thoughts

When dealing with mixed costs, start by identifying your variable and fixed components. Make sure to note the period of time your fixed cost is for (monthly, quarterly, annually, etc). Next write your cost equation. Finally, plug in your level of activity and solve.

Don’t let the slope formula throw you off. Remember that a mixed cost is just the sum of it’s fixed and variable components.

Fixed costs can be a tricky business. They might seem simple but if you think too much, you might get tripped up.

Just like with variable cost, fixed costs are named because of how the cost behaves in total. It is fixed. It does not change. Now most students will take that to mean that the cost will never change. If that were the case, there is not a fixed cost on the planet. All costs change over time. Remember, we are taking about how a cost behaves today.

A fixed cost does not have an activity or driver that makes the cost increase as the activity or driver increases. Let’s say you start a business and the rent for 500 square feet is $1000 per month for the first three years. Is there an activity or driver that would increase your rent expense?

Number of hours open? Nope

Number of customers per month? Nope

Amount of sales in units or dollars? Nope

And here is the most important question: if all of your drivers go to zero, does the cost go to zero as well? If you go on vacation for a month and close your business so there are no sales, no customers, nada is your rent expense zero? Nope

With a variable cost, when the driver was zero, the total variable cost was zero. With a fixed cost, that is not the case.

Remember our candy bar example from the post on variable cost? What if, in order to sell the candy bars on campus, you needed to pay a fee of $100 to the college. Is that a fixed cost or a variable cost? It is fixed because it does not change no matter how many (or how few) candy bars you sell.

Here is the graph for fixed cost:

Notice on this graph, there is no slope. The formula for total fixed cost = fixed cost. If looking at the equation for a line y = 0 + b, where b is equal to fixed cost. As long as you are within the relevant range, the formula is valid.

#### Related Videos

**Cost Behavior: Fixed, Variable, Step and Mixed **

**Fixed and Variable costs as per unit and total costs**

When thinking about cost behavior, think about how the cost behaves in total. A **variable cost** is a cost that varies in total. The cost increases or decreases based on a related activity.

The formula for total variable cost is:

**Total Variable Cost = Variable Rate X Activity**

### Assume a constant rate

For planning and decision making purposes, we assume that the variable rate is constant. This allows for a single variable in the calculations. Only the activity will change. Now, that is not always the case, but as long as we are within the relevant range for our decision, we can assume that the rate will stay the same.

### But isn’t it fixed if the rate stays the same?

Remember that a variable cost varies in total. The rate might stay the same but once you multiply the rate by varying levels of activity, the total variable cost will change.

Imagine that you are selling candy bars as a fundraiser for a club to which you belong. Your cost is 50 cents per candy bar and the club sells the candy bars for $1 each. If the club sells 200 candy bars, what is the total variable cost? Is it 50 cents? No, that is the cost of a single candy bar. If you sell 200, you would need to multiply that by 50 cents for each of the candy bars sold.

**200 candy bars X 50 cents per candy bar = $100**

What if the club sold 500 candy bars? The total variable cost would be $250.

Here is a graph of the total variable cost of candy bars for the fundraiser:

Notice that if no candy bars are sold, there is no cost. The more candy bars that are sold, the higher the cost. The cost line is a straight line. The slope of the line is equal to the variable rate. For each additional unit sold, the line increases at a rate of 50 cents. Think of the formula of a line: y=mx + b, where y is your y coordinate, x is your x coordinate, m is the slope and b is the y-intercept (the point where the line hits the y-axis).

The formula for total variable cost is: y=mx. The y-intercept for a variable cost is always zero because if there is no activity, there is no cost. Therefore, the line will always start at 0,0. The slope of the line, m, is your variable rate. The activity is x. See your math teacher was right when he or she told you you would use this stuff someday!

Frequently, you will see textbooks show the formula for the slope of a line as the formula for cost equations.

#### Related Videos

**Cost Behavior: Fixed, Variable, Step and Mixed **

**Fixed and Variable costs as per unit and total costs**