Mixed costs contain both a fixed component and a variable component. In order to determine the two components, managers must separate the mixed cost into the two cost components---fixed costs and variable costs. Breaking mixed costs into fixed and variable portions allows managers to use the costs to predict and plan for the future given the insight on that cost behavior provides. The process of separating mixed costs into fixed and variable components is referred to as cost estimation. This chapter will present four methods used by managers to estimate costs.

Cost Estimation Methods

The four methods of cost estimation to be covered in managerial accounting are listed below. The first three will be covered in this chapter, with regression covered in the next chapter.

Account analysis

Scatter graphs

High-low method

Linear regression

Cost estimation methods are necessary only for costs that are identified as mixed costs. There is no need to apply an estimation method to break a cost into fixed and variable portions if you have already determined it is solely fixed or solely variable. All four methods produce estimates of amounts of fixed and variable costs.

The Goal of Cost Estimation

The ultimate goal of cost estimation is to determine the amount of fixed and variable costs to create a cost formula to be used to predict future costs. The cost formula, or cost equation, is the output of the cost estimation process. Because you have only one variable (number of units), the formula will be a straight line, or linear equation. (You should remember the concept of functions from your middle school math classes.1) The formula that represents the equation of a line will appear in the format of:

Y = mx + b

where Y = total cost

m = the slope of the line, i.e., unit variable cost

X = the number of units of activity

b = the y-intercept, i.e., total fixed costs

Recall that the Y = VCx + TFC is the equivalent equation used in accounting for estimating costs. The total cost side of the equation (Y) can also be expressed as f(x) so that the formula appears as:

f(x) = VCx + TFC

As such, the equation is often referred to as a function. In accounting, it is referred to as a cost function because the 'Y' equates to total cost

Determining a linear function is useful in predicting cost amounts at different levels of activity. This is useful because managers must be able to predict costs to plan for future operations. This is often accompanied by what-if analysis that assists with the preparation of budgets, pricing of products or services, and other key management functions.

Cost Equation Components

Your goal it to determine the cost equation for a particular cost, so that managers can estimate 'total' costs at various activity levels. The cost equation will contain the variable cost per unit and total fixed costs. These two amounts remain the same at all levels of activity within the relevant range.

The variable cost component of the cost equation is displayed with two decimals in standard form because it is a unit cost (and unit costs are always displayed with two decimal places). The total fixed cost component of the cost equation is displayed with no decimals.

Account Analysis Method

The account analysis method of estimating fixed and variable costs is likely the approach you have used to identify cost behavior so far in your study of managerial accounting. This approach involves simply looking at a cost and guessing its most likely type of cost behavior. This method requires considerable subjective judgment and insight. It is most often used by accountants or managers who are familiar with the nature of costs within a general ledger account (often multiple accounts). Account analysis is the only method you can use to estimate costs when only one period of data is known.

The account analysis approach requires that each individual cost is examined, and based on judgment is categorized as a fixed or variable cost. Then all variable costs are totaled. Variable cost per unit is calculated by dividing the total of all variable costs by the number of units produced and sold.

 Total variable costs = Variable cost per unit Number of units produced and sold

The variable cost per unit is plugged into the cost formula as the variable cost (VC). The fixed costs are totaled separately to calculate the Y-intercept (TFC) component of the equation. This results in a cost equation that can be used to estimate costs for future periods.

Note that the determination of 'cost per unit' is literal. The calculation is performed exactly how it reads: 'Cost' is on the numerator; 'per' means divide; and 'units' appear on the denominator.

Walk Through Problem - Account Analysis

Home Shine is estimating its fixed and variable costs. The following costs were incurred during the month of May by Home Shine when 200 homes were cleaned:

 Cleaning supplies \$ 2,400 Hourly wages 4,850 Depreciation - cleaning equipment 650 Manager’s salary 1,400 Auto commuting expenses 1,600 Office rent 850 Total costs \$11,750

Use the account analysis method to determine the total cost equation for Home Shine.

Solution

Step 1: Classify each cost as variable or fixed based on judgment. By definition, variable costs increase in total when more activity occurs. By definition, fixed costs are the same in total regardless of the activity level. The activity for this problem is number of homes cleaned.

Cleaning supplies = variable cost. The total cost of cleaning supplies increases when more homes are cleaned.

Hourly wages = variable cost. The total cost of hourly wages increases when more homes are cleaned.

Depreciation = fixed cost. The total cost of depreciation is \$650 regardless of the number of homes cleaned.

Manager's salary = fixed cost. The manager's salary is the same regardless of the number of hours worked or the number of homes cleaned.

Auto commuting expenses = variable cost. The total cost of commuting expenses such as gasoline and maintenance increases when more homes are cleaned.

Office rent = fixed cost. The monthly office rent is the same regardless of the number of homes cleaned.

Step 2: Add the costs you identified as variable.

\$2,400 + \$4,850 + \$1,600 = \$8,850

Calculate variable cost per unit by dividing the total of the variable costs by the number of units (homes) produced and sold (homes cleaned).

 \$8,850 = \$44.25 200

Step 3: Add the costs you identified as fixed costs.

\$650 + \$1,400 + \$850 = \$2,900

Step 4: Plug your answers to steps 2 and 3 into the cost formula by replacing the slope with the variable cost per unit and the Y-intercept with total fixed costs:

Y = 44.25x + 2,900

The cost equation indicates that the total cost of cleaning homes is \$44.25 per home plus a monthly cost of \$2,900.

Scatter Graph Method

Creating a scatter graph is another method of estimating fixed and variable costs. It provides a visual picture of the total costs at different activity levels. However, it is often hard to visualize the cost equation line through the data points, especially if the data is varied. This approach requires multiple data points and requires five steps:

Step 1: Draw a graph with the total cost on the y-axis and the activity (units) on the x-axis. Plot the total costs for each activity point.

Step 2: Visualize and draw a straight line through the data points.

Step 3: Determine variable cost per unit by identifying the slope thorough a measure of rise over run.

 Rise = Variable cost per unit Run

'Rise' is the difference in total costs and 'run' is the difference in number of homes cleaned.

Step 4: Identify where the line crosses the y-axis. This is the total fixed cost amount.

Step 5: Plug your answers to steps 3 and 4 into the cost formula in the following format:

Y = VCx + TFC

If you have forgotten how to graph data points, review graphing concepts here.1

High-Low Method

The high-low method uses the highest and lowest activity levels of a data set to estimate the portion of a mixed cost that is variable and the portion that is fixed. Because this method uses only the high and low activity levels to calculate the variable and fixed costs, it may be misleading if the activity levels are not representative of the normal activity, i. e., they may be extremes, or outliers. For example, if most data points lie in the range of 60 to 90 percent for a particular accounting test, and one student scored a 20 percent, the use of the low point will distort the actual expectation of grades in the future. The high-low method is most accurate when the costs incurred at the high and low levels of activity are representation of the majority of the other data points. The steps that follow will guide you through the high-low method:

Step 1: Determine which data represents the total cost (dependent variable, Y) and which represents the activity (independent variable, x). Find the lowest and highest activity points in the data representing the x variable.

Step 2: Determine variable costs per unit by using the mathematical slope formula which divides the change in cost by the change in activity:

 Y2 - Y1 = Variable cost per unit X2 - X1

Where X2 is the high activity level

X1 is the low activity level

Y2 is the total cost at the high activity level

Y1 is the total cost at the low activity level

Step 3: Plug your answer to step 2 and the amounts from either the high or the low data point into the cost formula by replacing the 'VC' with the variable cost per unit. Using the high data point, plug the total cost (at the highest activity point) into the Y variable, and the high activity point for the x variable. Then solve for total fixed costs, 'TFC'.

Step 4: Plug your answers to steps 2 and 3 into the cost formula by replacing the slope (VC) with variable cost per unit and the y-intercept (TFC) with total fixed costs in the following format:

Y = VC x + FC

If you have forgotten algebra concepts relating to the slope-intercept form, you can review those concepts here.2

Walk Through Problem - High-Low Method

Information concerning units sold and total delivery costs for Bridges, Inc. for five months of 2018 appears below:

 Month Units Costs January 1,200 \$74,150 February 1,150 71,000 March 1,190 72,400 April 1,300 80,600 May 1,310 79,040

Use the high-low method to answer the following:

A.  How much is the variable cost per unit?

B.  How much are total fixed costs?

C.  Write the cost equation in proper form.

Solution

q Step 1: The Units column contains the activity data. The Costs column contains the total cost data. Select the high and low data points from the Units column. The largest activity was generated in May with 1,310 units, while  the lowest activity was generated in February with 1,150 units.

q

Step 2: Use the slope formula by subtracting the smallest from the largest activity on the denominator. Use the corresponding total costs for May and February and subtract the smallest from the largest cost on the numerator:

 Y2 - Y1 = \$79,040 - \$71,000 = \$50.25 per unit Y2 - Y1 1,310 - 1,150

The variable cost per unit is \$50.25.

Step 3: Select either of the two data points that you chose in Step 1 to plug into the cost equation. Both data points will result in the same answer. Using the low data point (February), the total cost of \$71,000 is substituted for “Y” in the cost equation, and 1,150 units is substituted for 'x'. Substitute the unit variable cost from step 2 into the formula for “VC.” You should now have the following equation:

Y = VCx + TFC

71,000 = (50.25 x 1,150)  + TFC

Solve for total fixed costs (TFC), which results in \$13,212.50.

Step 4:  Write the cost formula in standard form by plugging in the variable cost per unit and total fixed costs as follows:

TC = 50.25x + 13,213

The standard format is to express variable cost per unit using two decimal places and total fixed costs with no decimal places.

Using a Cost Equation to Estimate Future Costs

Once a cost equation is determined, it can be used to estimate costs at various levels of activity. For example, assume Bridges, Inc. expects to sell 1,240 units of product in June. Using the total cost equation determined in the high-low method walk through problem, the total estimated cost will be:

Total cost = (50.25 x 1,240) + 13,213 = \$75,523

Bridges, Inc. estimates that the total delivery cost for June will be \$75,523.

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