Chapter 5
Cost Estimation
Cost Estimation Methods
Mixed costs have both a fixed portion and a variable portion. There are a handful of methods used by managers to break mixed costs in the two manageable components--fixed costs and variable costs. The process of breaking mixed costs into fixed and variable portions allow us to use the costs to predict and plan for the future since we have a good insight on how these costs behave at various activity levels. We often call the process of separating mixed costs into fixed and variable components, cost estimation.
The four methods of cost estimation to be discussed are listed below, with regression covered in chapter 6 and the others in this chapter:
Account analysis
Scatter graphs
High-low method
Linear regression
The Goal of Cost Estimation
The ultimate goal of cost estimation is to determine the amount of fixed and variable costs so that a cost equation can be used to predict future costs. You should remember the concept of functions from your business calculus class. The function that represents the equation of a line will appear in the format of:
y = m x + b
where y = total cost
m = the slope of the line, i.e., the unit variable cost
x = the number of units of activity
b = the y-intercept, i.e., the total fixed costs
Determining a linear function is useful in predicting cost amounts at different levels of activity. Why do managers need to be able to predict costs? They want to plan for future operations often through what-if analysis and budgets. A key concept you must remember is that before you employ any of the estimation methods, you must have already determined the cost is mixed. There is no need to analyze a cost to break it down into fixed and variable portions if you already know whether it is variable or fixed. Your goal it to determine the variable cost per unit and total fixed costs to plug into the cost equation.
Helpful Hint: Note that the determination of 'cost per unit' is literal. When you read this label, write the equation exactly how it reads: Cost is on the numerator' Per means divide; and units appears on the denominator.
Account Analysis
One method of estimating fixed and variable costs requires considerable subjective judgment. This is likely the approach you have taken to identify cost behavior so far in your study of managerial accounting by looking at a cost and guessing its most likely type of cost behavior. It is most often used by accountants or managers who are familiar with the costs within an account. Account analysis is the only method you can use to estimate costs when only one data point is known. The account analysis approach requires four steps:
Step 1: Look through the costs that are included in a particular account and classify each amount as variable or fixed based on judgment.
Step 2: Total the variable costs. Determine variable costs per unit by dividing the total of all the variable costs you identified by the number of units produced (or sold). This will give you the cost per unit.
Total Variable Costs | = Variable cost per unit |
# of Units Produced |
Step 3: Total the fixed costs.
Step 4: Plug your answers to steps 2 and 3 into the cost formula by replacing the slope (m) with variable cost per unit and the y-intercept (b) with total fixed costs in the following format:
y = m x + b
Scatter Graph Approach
Creating a scatter graph is another method of estimating fixed and variable costs. It provides a good visual picture of the costs at different activity levels. However, it is often hard to visualize the 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 cost points for each activity points.
Step 2: Visualize and draw a straight line through the points.
Step 3: Determine variable costs per unit by identifying the slope thorough a measure of rise over run.
Rise | = Variable cost per unit |
Run |
Step 4: Identify where the line crosses the y-axis. This is the total fixed cost.
Step 5: Plug your answers to steps 3 and 4 into the cost formula by replacing the slope (m) with variable cost per unit and the y-intercept (b) with total fixed costs in the following format:
y = m x + b
Note:
If you have forgotten how to graph data points, this will help. . http://www.studyzone.org/testprep/math4/d/linegraph4l.cfmSource www.studyzone.org Grade 4 Math Lessons
High-Low Method
The high-low method uses the highest and lowest activity levels over a period of time to estimate the portion of a mixed cost that is variable and the portion that is fixed. Like the account analysis and scatter graph method, the amounts determined for fixed and variable costs are only estimates. Because it uses only the high and low activity levels to calculate the variable & fixed costs, it may be misleading if the high and low activity levels are not representative of the normal activity. 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, the use of the low point might distort the actual expectation of costs in the future. The high-low method is most accurate when the high and low levels of activity are representation of the majority of the other points. The steps below guide you through the high-low method:
Step 1: Determine which set of data represents the total cost and which represents the activity. Find the lowest and highest activity points.
Step 2: Determine variable costs per unit by using the mathematical formula for a slope where you take divide 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 selected
Y1 is the total cost at the low activity level selected
Step 3: Plug your answer to steps 2 along with either the high or the low point into the cost formula by replacing the slope (VC) with variable cost per unit, the high activity total cost for the y variable, and the high activity for the x variable. Then solve for fixed costs (FC).
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 (FC) with total fixed costs in the following format:
y = VC x + FC
High Low Example:
Information concerning units sold and total costs for Bridges, Inc. for five months of 2009 appears below:
|
|
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 are variable costs per unit?
B. How much are total fixed costs?
C. Write the cost equation in proper form:
Solution:
qStep 1: Select the high and low data activity points. Because the Units column represents activity, select the high point: May, and the low point: February.
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
x2 - x1
1,310 - 1,150
This is the variable cost per unit.
Step 3: Pick one point. They will both result in the same final answer. Substitute the total cost of one of the points for “y” in the equation: y = mx + b. Using the low point of February, total costs are $71,000 total cost at 1,150 units. Substitute the variable cost from step 2 into the formula for “m.” Substitute the number of activity units for the low data point for “x” You should now have the following equation:
71,000 = $50.25*1,150 + b
Solve for total fixed costs which is the “b” variable, which gives you $13,212.50.
Step 4: Determine the cost formula to use in estimating the mixed costs at various levels in the following format by plugging in the variable cost per unit and total fixed cost by plugging the variable cost per unit and the total fixed costs into the cost equation as follows:
y = $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.
A few words about variable cost per unit.....
Variable cost per unit is very literal meaning you determine 'cost per unit' using the literal interpretation:
In determining cost per unit, cost comes first so place it on the numerator. Per means to divide so draw the division sign under 'cost'. Unit comes last so it belongs on the denominator.
Cost | = Variable cost per unit |
Unit |
When you determine variable cost per unit, you must take the total cost and divide by number of units. In accounting, we often use the following as cost per unit amounts:
machine hours per unit
profit per sales dollar
cost per labor hour
miles per hour