Mixed Costs

Mixed costs, also called semi-variable costs, are costs that include both a fixed component and a variable component. The fixed part must be paid even when activity is zero, while the variable part rises and falls with the level of activity, such as units produced, hours worked or miles driven. A typical example is a utility bill made up of a fixed monthly service charge plus a charge for each kilowatt-hour used.

Mixed costs are an important part of cost behavior analysis in managerial accounting. Budgets, break-even calculations and pricing decisions all require costs to be classified as fixed or variable, so mixed costs must first be split into their two parts. They sit between purely fixed costs, such as rent, and purely variable costs, such as raw materials.

• Utilities, with a fixed connection or standing charge and a usage-based charge.
• Sales compensation, made up of a base salary plus commission on sales.
• Vehicle costs, combining fixed insurance and registration with fuel and maintenance that depend on mileage.
• Equipment maintenance, with a fixed service contract and extra charges for repairs linked to usage.
• Telephone and cloud computing plans, with a fixed monthly fee and charges for use above an allowance.

A mixed cost can be described by a cost equation:

• $Y$ is the total cost for the period.
• $a$ is the fixed cost component.
• $b$ is the variable cost per unit of activity.
• $X$ is the level of activity.

The simplest way to estimate $a$ and $b$ from past data is the high-low method. Suppose a factory's maintenance costs were $14,000 in its quietest month, when machines ran 2,000 hours, and $26,000 in its busiest month, at 6,000 hours. The variable cost per hour is the change in cost divided by the change in activity: $12,000 divided by 4,000 hours, which is $3 per hour. The fixed cost is total cost minus the variable part at either point: $14,000 minus (2,000 times $3), which is $8,000 a month. The cost equation is therefore $8,000 plus $3 per machine hour, so at 4,500 hours the expected cost is $8,000 plus $13,500, or $21,500.

The high-low method uses only two data points, which may be unusual months. More accurate approaches are the scatter-graph method, which plots all observations to judge the trend visually, and least-squares regression, which fits the line that best explains all the data. Accounting software and spreadsheets make regression easy to apply.

Once split, mixed costs can be used in a flexible budget, which adjusts the expected cost to the actual level of activity. In the example, a plant that runs 5,000 hours should expect maintenance of $23,000; a bill of $25,000 would show a $2,000 overspend worth investigating. The fixed and variable parts also feed cost-volume-profit (CVP) analysis: the variable part reduces the contribution margin per unit, while the fixed part adds to the fixed costs that must be covered to reach the break-even point.

The fixed-plus-variable model is a simplification that holds only within a relevant range of activity. Outside that range, a cost may behave differently: a utility might charge a higher rate above a certain usage level, or a second shift might require extra supervisors, creating a step in fixed costs. Past data can also mislead if prices, technology or processes have changed. Some costs that appear mixed are really step costs that rise in blocks. Despite these limits, splitting mixed costs is a basic step in cost accounting, and much factory overhead is analyzed in exactly this way.