Short-Term Decision-Making

Question: We have now learned about two types of cost behavior patterns– variable costs and fixed costs. However, there is a third type of cost that behaves differently in that both total and per unit costs change with changes in activity. What do we call this type of cost?

Answer: This cost behavior pattern is called a mixed cost. The term mixed cost describes a cost that has a mix of fixed and variable costs. For example, assume sales personnel at Bikes Unlimited are paid a total of $10,000 in monthly salary plus a commission of $7 for every bike sold. This is a mixed cost because it has a fixed component of $10,000 per month and a variable component of $7 per unit.

Table 5.3 "Mixed Cost Behavior for Bikes Unlimited" provides the total and per unit fixed costs at three different levels of production, and Figure 5.3 "Total Mixed Sales Compensation Costs for Bikes Unlimited" graphs the relation of total mixed costs (y-axis) to units produced (x-axis). The point at which the line intersects the y-axis represents the total fixed cost ($10,000), and the slope of the line represents the variable cost per unit ($7).

Table 5.3 Mixed Cost Behavior for Bikes Unlimited

Figure 5.3 Total Mixed Sales Compensation Costs for Bikes Unlimited

Because this cost is depicted with a straight line, we can use the equation for a straight line to describe a mixed cost:

Key Equation

Total mixed cost = Total fixed cost + (Unit variable cost × Number of units)

or

Y = f + vX

where

Y = total mixed costs (this is the y-axis in Figure 5.3 "Total Mixed Sales Compensation Costs for Bikes Unlimited")

f = total fixed costs

v = variable cost per unit

X = level of activity (this is the x-axis in Figure 5.3 "Total Mixed Sales Compensation Costs for Bikes Unlimited")

For Bikes Unlimited, the mixed cost equation is Y = $10,000 + $7X. If Bikes Unlimited sells 4,000 bikes (X) in one month, the total mixed cost (Y) for sales personnel compensation would be $38,000 [= $10,000 + ($7 × 4,000 units)].