# What are mixed costs?

## Definition of Mixed Costs

In accounting, the term mixed costs refers to costs and expenses that consist of two components:

• A fixed component, the total of which does not change as the volume of activity changes
• A variable component, the total of which changes in proportion to the change in the volume of activity

A mixed cost is also referred to as a semivariable cost.

A mixed cost is expressed by the algebraic formula y = a + bx, where:

• y is the total cost
• a is the fixed cost per period
• b is the variable rate per unit of activity
• x is the number of units of activity

To visualize the behavior of a mixed cost, it is helpful to graph at least 8 observations. Each observation's total cost (y) is aligned with the y-axis and is also aligned with the volume amounts indicated on the x-axis. To compute the best fitting line through the graphed data, you could use a mathematical tool known as simple linear regression analysis. This will calculate the fixed expenses (a) and the variable rate (b) based on the historical observations.

## Example of Mixed Costs

The annual expense of operating an automobile is a mixed cost. Some of the expenses are fixed because they do not change in total as the number of annual miles change. These include insurance, parking fees, and some depreciation. Some of the expenses are variable since the total amount will increase when more miles are driven and will decrease when fewer miles are driven. The variable expenses include gas, oil, tires, and some depreciation.

Let's assume that a simple linear regression analysis indicates that the past annual expense of operating an automobile (y) consisted of the fixed cost (a) of \$5,000 per year and the variable rate (b) was \$0.20. When the number of miles driven during a year (x) are 15,000 miles, the expected total annual expense is the fixed expense \$5,000 + the variable expense of \$0.20 X 15,000 = \$5,000 + \$3,000 = \$8,000. If the miles driven are 10,000 miles, the expected total annual expense is the fixed expense of \$5,000 + the variable expense of \$0.20 X 10,000 = \$5,000 + \$2,000 = \$7,000.