Mixed Costs: Videos & Practice Problems

If a company’s costs are all mixed costs, which of the following quantities will result in the lowest average mixed cost?

• A. 5,000 units
• B. 10,000 units
• C. 15,000 units
• D. All the above will result in the same average variable cost.

Answer: (C)

A mixed cost’s equation is estimated to be Y = 7X + 500. What is the value of the fixed component of this mixed cost?

• A. 7
• B. 7X
• C. 500
• D. X

Answer: (C)

Here's what students ask on this topic:

What is the definition of mixed costs in managerial accounting?

Mixed costs in managerial accounting are expenses that contain both fixed and variable components. This means part of the cost remains constant regardless of the activity level, while the other part changes in direct proportion to the level of activity. For example, a maintenance fee might have a fixed base charge plus a variable charge depending on usage. The total mixed cost increases as activity increases but does not start at zero because of the fixed portion. The standard equation representing mixed costs is $Y=BX+A$, where $A$ is the fixed cost and $BX$ is the variable cost component.

How do you graph mixed costs and what does the graph look like?

When graphing mixed costs, the line starts at a point above zero on the y-axis because of the fixed cost component. As activity level increases along the x-axis, the total mixed cost rises, similar to a variable cost. The graph is a straight line with a positive slope, reflecting the variable portion, and a y-intercept equal to the fixed cost. This means the cost increases as activity increases but never starts at zero. The equation for the line is $Y=BX+A$, where $A$ is the fixed cost (y-intercept) and $B$ is the variable cost per unit (slope).

What happens to the average mixed cost per unit as activity level increases?

The average mixed cost per unit decreases as the activity level increases. This is because the fixed cost component is spread over more units, reducing the fixed cost per unit. The average mixed cost per unit is calculated as $\frac{Y}{X}=B+\frac{A}{X}$. As $X$ (activity level) increases, the term $\frac{A}{X}$ becomes smaller, causing the average cost to approach $B$, which is the average variable cost per unit. Unlike average fixed cost, the average mixed cost per unit never reaches zero but levels off at the variable cost per unit.

How is the mixed cost equation related to the linear equation learned in algebra?

The mixed cost equation $Y=BX+A$ is structurally the same as the linear equation from algebra, $Y=MX+B$. In this context, $B$ in the mixed cost equation corresponds to the slope $M$ in algebra, representing the variable cost per unit, and $A$ corresponds to the y-intercept $B$, representing the fixed cost. This similarity helps in understanding how mixed costs behave as activity changes, combining both fixed and variable elements in a linear relationship.

Why can't we simply cancel out the activity level variable when calculating average mixed cost per unit?

When calculating average mixed cost per unit, the total mixed cost is divided by the activity level $X$, giving $\frac{Y}{X}=B+\frac{A}{X}$. We cannot cancel out $X$ because the fixed cost component $A$ is not multiplied by $X$. Only the variable cost part $BX$ includes $X$. Therefore, when dividing total cost by $X$, the fixed cost portion becomes $\frac{A}{X}$, which decreases as $X$ increases, but cannot be canceled out.