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.
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
$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
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.
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
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
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.
Cost Behavior: Fixed, Variable, Step and Mixed
Fixed and Variable costs as per unit and total costs
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 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.
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 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.
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.
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.
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.
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.
Cost Behavior: Fixed, Variable, Mixed and Step Costs