The algebraic formula for a mixed cost is 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, and x is the number of units of activity. For the annual expense of operating an automobile, the fixed cost, a, might be $5,000 per year; the variable rate, b, could be $0.20; and the number of units of activity, x, might be 15,000 miles per year. With these hypothetical assumptions, the annual expense, y, would be $8,000. If x were 10,000 miles, the annual expense y would be $7,000.
To gain insight on the behavior of a mixed cost, it is helpful to graph the cost: For each observation, indicate a point on the graph where the total mixed cost amount aligns with the amounts on y-axis and also aligns with the activity amounts on the x-axis. To compute the best fitting line through the graphed data, you could use a mathematical tool known as regression analysis. This will calculate the fixed expenses, a, and the variable rate, b, based on the historical data that is utilized.
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