It is perhaps the simplest technique for separating a

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Unformatted text preview: ponents. 2.2 High-Low Method One approach to sorting out mixed costs is the high-low method. It is perhaps the simplest technique for separating a mixed cost into fixed and variable portions. However, beware that it can return an imprecise answer if the data set under analysis has a number of rogue data points. But, it will work fine in other cases, as with the water bills for Butler’s Car Wash. Information from Butler’s actual water bills is shown at above right. Butler is curious to know how much the August water bill will be if 650,000 gallons are used. Assume that the only data available are from the aforementioned four water bills. With the high-low technique, the highest and lowest levels of activity are identified for a period of time. The highest water bill is $3,550, and the lowest is $2,020. The difference in cost between the highest and lowest level of activity represents the variable cost ($3,550 - $2,020 = $1,530) associated with the change in activity (850,000 gallons on the high end and 340,000 gallons on the low end yields a 510,000 gallon difference). The cost difference is divided by the activity difference to determine the variable cost for each additional unit of activity ($1,530/510 thousand gallons = $3 per thousand). The fixed cost can be calculated by subtracting variable cost (per-unit variable cost multiplied by the activity level) from total cost. The table at above right reveals the application of the high-low method. An electronic spreadsheet can be used to simplify the high-low calculations. The website includes a link to an illustrative spreadsheet for Butler. Download free ebooks at 15 Cost Behavior Analysis Cost Analysis 2.3 Method of Least Squares As cautioned, the high-low method can be quite misleading. The reason is that cost data are rarely as linear as presented in the preceding illustration, and inferences are based on only two observations (either of which could be a statistical anomaly or “outlier”). For most cases, a more precise analysis tool should be used. If you have studied statistical methods, recall “regression analysis” or the “method of least squares.” This tool is ideally suited to cost behavior analysis. This method appears to be imposingly complex, but it is not nearly so complex as it seems. Let’s start by considering the objective of this calculation. The goal of least squares is to define a line so that it fits through a set of points on a graph, where the cumulative sum of the squared distances between the points and the line is minimized (hence, the name “least squares”). Simply, if you were laying out a straight train track between a lot of cities, least squares would define a straight-line route between all of the cities, so that the cumulative distances (squared) from each city to the track is minimized. Please click the advert Let’s dissect this method, beginning with the definition of a line. A line on a graph can be defined by its intercept with the vertical (Y) axis and the slope along the horizontal (X) axis. In the following diagram, observe a red line starting on the Y axis (at the value of “2”), and rising gently upward as it moves out along the X axis. The rate of rise is called the slope of the line; in this case, the slope is 0.8, because the line “rises” 8 units on the Y axis for every 10 units of “run” along the X axis. Download free ebooks at 16 Cost Behavior Analysis Cost Analysis In general, a straight line can be defined by this formula: Y = a + bX where: a = the intercept on the Y axis b = the slope of the line X = the position on the X axis For the line drawn on the previous page, the formula would be: Y = 2 + 0.8X And, if you wished to know the value of Y, when X is 5 (see the red circle on the line), you perform the following calculation: Y = 2 + (0.8 * 5) = 6 Now, lets move on to fitting a line through a set of points. On the next page is a table of data showing monthly unit production and the associated cost (sorted from low to high). These data are plotted on the graph to the right. Through the middle of the data points is drawn a line, and the line has a formula of: Y = $138,533 + $10.34X Download free ebooks at 17 Cost Behavior Analysis Cost Analysis This formula suggests that fixed costs are $138,533, and variable costs are $10.34 per unit. For example, how much would it cost to produce about 110,000 units? The answer is about $1,275,000 ($138,533 + ($10.34 * 110,000)). How was the formula derived? One approach would be to “eyeball the points” and draw a line through them. You would then estimate the slope of the line and the Y intercept. This approach is known as the scatter graph method, but it would not be precise. A more accurate approach, and the one used to derive the above formula, would be the least squares technique. With least squares, the vertical distance between each point and resulting line (e.g., as illustrated by an arrow at the $1,500,000 point...
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This note was uploaded on 06/07/2013 for the course BA 201 taught by Professor Cuongvu during the Fall '13 term at RMIT Vietnam.

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