- Explain how to diagnose Cost Behavior with a Scattergraph Plot - Explain how to use the High-Low Method for Analysis - Explain how to use the Least-Squares Regression Method [SLIDE 1] Managerial accountants have several options when trying to analyze mixed costs for the organization. This analysis is necessary in order for management to plan, control and make decisions regarding the direction of the company. In order to analyze mixed costs for planning and control, managerial accountants and managers have to separate the fixed costs from the variable costs. One way to do this is by account analysis, where based on prior knowledge of how the cost behaves, they classify it as fixed or variable. The fixed portion of mixed cost is the minimum cost of having a service or product ready and available for use. The variable portion is the cost incurred for actual consumption of the service or product and will vary in proportion to the amount actually consumed. The more accurate the division of fixed and variable cost is, the more accurate the analysis of mixed cost will be for planning and control of the organization. Managerial accountants and managers can also use the following three methods to perform separation analysis of fixed and variable costs that we will discuss in this lesson:
  1. Scattergraph Plot
  2. High-Low Method
  3. Least-Squares Regression Method
[SLIDE 2] The scattergraph method considers all data points and is also called a quick and dirty method to isolate fixed and variable cost in mixed costs. Accountants and managers use this to diagnose cost behavior and to perform further analysis using High-Low and Least-squares regression methods. The scattergraph method involves 5 steps to analyze mixed costs for fixed and variable components.
  1. Plot data points on the graph using cost as the dependent variable plotted on the "Y-axis" and the activity as the independent variable on the "X-axis".
  2. Visually review the plotted points on the graph and determine if a linear relationship exists between the activity and the cost.
  3. Estimate the total fixed costs (f). Fixed cost is the point at which the line intersects the "Y-axis" and is considered the y-intercept. This is the point at which the activity level is zero and there is no variable cost being incurred. In the graph shown, the fixed cost is estimated at $45,000 when there is no activity.
  4. Calculate the variable cost per unit (v). Using a data point that intersects on the line, you can use the formula Y = f + vX to calculate the variable cost at the selected data point. In the graph shown, let's choose the data point 3,500 units produced and $230,000 in cost. By applying the information for the known variables, Y, f and X, we can calculate the variable cost per unit: 230,000 = 45,000 + v(3,500) 230,000 - 45,000 = v(3,500) 185,000 = v(3,500) 185,000/3,500 = v ~52.86 = v (rounded) The variable cost is approximately $52.86 per unit.
  5. State the results in equation form Y = f + vX. In this example the formula would be Y = 45,000 + 52.86X. Using this formula, the managerial accountant or manager can estimate total production costs when given a certain level of production.
While the scattergraph tends to yield more accurate results, the final cost equation is still based on estimates. This approach is not exact but yields a good estimate for further data analysis and organizational planning. [SLIDE 3] The High-Low method considers the lowest and highest activity levels to isolate fixed and variable cost in mixed costs. This method should only be used if the scattergraph plot confirms that a linear relationship exists between the cost and the activity. If a linear relationship does not exist, then the estimate would not be useful in further planning or control analysis. The high-low method involves 4 steps to analyze mixed costs for fixed and variable components.
  1. Plot data points on the graph using cost as the dependent variable plotted on the "Y-axis" and the activity as the independent variable on the "X-axis". While plotting them on a graph is not necessary, it is a helpful visual tool. Select the lowest and highest activity points from the data set used in the analysis. In the graph shown, the lowest level of activity is 2,900 units with $200,000 in production costs and the highest is 5,900 units with $380,000 in production costs. Remember, we are looking at activity levels -- not cost -- because cost will yield incorrect activity levels and incorrect costs per unit.
  2. Calculate the variable cost per unit (v). Using the high and low data points from step 1, we will calculate the slope of the line (rise over run) to arrive at the variable cost per unit. We take the difference in the cost and divide by the difference in the activity to get the per unit variable cost. The formula is Variable Cost = Change in cost / Change in activity. v = (380,000-200,000) / (5,900-2,900) v = 180,000 / 3,000 v = 60 This gives us a variable cost of $60.00 per unit.
  3. Calculate the total fixed costs (f). Select either the low or high activity level to calculate the total fixed cost using the formula Y = f + vX. Using the lowest activity level of $200,000 cost and 2,900 production units, we arrive at a total fixed cost of $26,000: 200,000 = f + 60(2,900) 200,000 – 174,000 = f 26,000 = f
  4. State the results in equation form Y = f + vX. In this example, the formula would be Y = 26,000 + 60X. Using this formula, the managerial accountant or manager can estimate total production costs when given a certain level of production.
While the high-low method uses only two data points to establish estimates for fixed and variable costs, it may not represent the data set as a whole and can distort the estimates. This approach, like the scatterplot, is not exact but can yield a good estimate for further data analysis and organizational planning. [SLIDE 4] The least-squares regression method is a statistical method that measures the average amount of change in the dependent variable associated with a unit change in one or more independent variables. This method minimizes the sum of the squared vertical differences from the data point to the regression line. The vertical difference, called the residual term, measures the distance between actual cost and estimated cost for each observation. The smaller the residual terms, the better the fit between the actual cost observation and the estimated cost. This method uses complex formulas to calculate the fixed and variable costs using all of the data points and can be quickly performed using computer software such as Excel. The calculated fixed and variable costs can then be added to the equation we used for scatterplot and high-low, Y = f + vX, to predict cost changes when the activity level changes. This method is the most accurate analysis of mixed cost and uses all the data points to estimate the fixed and variable cost. Accurate cost estimation helps managers predict future costs and evaluate the success of planning initiatives. [SLIDE 5] As you can see in the example, Regression Analysis tends to be the most accurate because it provides a cost equation that best fits the line to the data points. However, the goal of most companies is to get close -- the results do not need to be perfect. Each method has its advantages and disadvantages, and the choice of a method will depend on the situation at hand. If a quick estimate is needed, the high-low method may be appropriate. The scattergraph method helps with identifying any unusual data points which can be thrown out when estimating costs. Finally, regression analysis can be run using computer software such as Excel and generally provides for more accurate cost estimates. Being able to analyze mixed costs helps managerial accountants and managers better predict outcomes when cost or activity levels change. This also increases the ability for an organization to adjust when changes occur to meet the needs of their customers.