cost behavior

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:

Total 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.

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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:

Total Variable Cost

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.

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The idea of cost behavior is one of the most important concepts in managerial accounting. Determining how a cost will behave is critical to planning, decision making and controlling. Two types of costs are discussed in this post: variable costs and fixed costs. These types of costs get their names because of how they behave when we look at the costs in total.

Variable Costs

Variable costs are costs that increase incrementally as a driver increases. A driver is an activity or event that causes a cost to increase. All variable costs must have a driver. Two of the most common drivers used in managerial accounting are units and hours, but there are lots of different drivers that could be used like customers or miles. If you can determine that a cost is driven by a particular activity, you can use that driver to calculate a variable cost.

A variable cost must have a rate. The rate is expressed as a cost per unit of the driver. For example, direct labor costs are expressed as dollars per direct labor hour. To calculate the total variable cost, multiply the rate by the units of activity.

Total Variable Cost = Rate x Activity

In our planning and decision making calculations, we assume that the variable rate stays the same. Only the driver increases or decreases. Because the rate stays the same, the cost will increase by the amount of the rate for each additional unit of activity. All variable costs will be zero if there is no activity.

Example #1

Direct materials cost per unit of a product is $4 per unit. What is the total cost of direct materials if 1,000 units are produced? What if 2,500 units are produced?

Direct materials are a variable cost. We have a rate and a driver. The driver in this case is units. For each unit that is produced, the total cost of direct materials increases by $4.

To calculate the total cost of materials, take the rate and multiply by the activity.

$4 per unit X 1,000 units = $4,000

$4 per unit X 2,500 units = $10,000

Yes, it is really that easy.

Some other variable costs include direct labor, variable manufacturing overhead, and variable selling costs.

Fixed Costs

Fixed costs are costs that do not change as activity levels increase. Fixed costs do not have a driver. Most fixed costs are expressed in terms of time, like per month or per year. No matter what happens during that time, the cost stays the same. If the company pays $12,000 per month for rent, it does not matter if the company produces no units or is at maximum capacity. The rent is the same.

Sometimes, fixed costs are expressed as a per unit cost or a per hour cost for a certain level of activity. These leads people to believe that these are actually variable costs. It is possible to express a fixed cost on a per unit basis but remember that the total cost is not driven by that activity. The total cost is still the same no matter how many units of activity occur.

Example #2

Fixed manufacturing overhead costs are estimated to be $5 per unit for 10,000 units. What is the total manufacturing overhead cost for 12,000 units assuming that the companies manufacturing capacity is 15,000 units?

When quickly looking at the example, it would appear that the manufacturing costs are variable because they are expressed as a per unit rate. However, this rate is only valid when 10,000 units are produced because we are told that the cost is fixed.

To calculate the total fixed overhead, multiply the rate by the number of units for which that rate applies.

$5 per unit X 10,000 units = $50,000

Because this cost is fixed, the total cost will be the same for 12,000 units as it is for 10,000 units. Remember, fixed costs are fixed in total!

What happens to the rate as we produce more units? Let’s take a look.

Example #3

Using the solution from Example #2, calculate the fixed cost per unit for 12,000 units.

Will the per unit rate for fixed manufacturing overhead be the same if we produce 12,000 units instead of 10,000 units? No, it won’t. That’s because we are taking the same total cost and allocating it over more units. Therefore, the per unit cost will fall.

To calculate the per unit cost, take the total cost and divide it by the number of units.

$50,000 / 12,000 units = $4.17 (rounded)

The cost per unit is lower for 12,000 units than for 10,000 units because the total costs stay the same.

Relevant Range

When we make these assumptions about cost, we have to consider the relevant range. Relevant range is the range of activity in which the assumptions are true. If the activity is outside the relevant range, then cost assumptions about variable rate and fixed cost will change.

For example, if the company pays $12,000 per month for rent and the maximum production capacity because of space limitations is 15,000 units, what happens when the company wants to make 16,000 units? Well, the company can’t make 16,000 units in its current space. If it wanted to make an additional 1,000 units, the company would need to rent additional space or move to a new space. Producing 16,000 units is outside the relevant range and therefore $12,000 per month for rent would no longer be valid at that production level. The relevant range for the rent is zero units produced to 15,000 units produced.

Final thoughts

When considering how a cost behaves, look at how the cost behaves in total. Variable costs vary in total based on the level of activity. If there is no activity the total cost is zero. Fixed costs do not change based on activity. The cost will stay the same in total as long as activity is within the relevant range. Because fixed costs are fixed in total, the per unit rate will change as production changes. The higher the level of production, the lower the per unit rate will be because a fixed amount of money is being spread out among more units.

Another way to look at it is:

Variable rate does not change, but total variable cost does change as activity changes.

Total fixed costs do not change, but fixed rate does change as activity changes.

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