relevant range

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.

 Related Videos

Cost Behavior: Fixed, Variable, Mixed and Step Costs

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