[Music] I'm Larry Walther this is chapter 18 of principles of accounting comm in the previous module we considered the definitions of fixed cost and variable cost and some of the implications for a business in terms of understanding those cost in this module however we are going to consider how we would determine the fixed and variable nature of cost for a particular business in other words we're going to look at cost behavior now some costs are not strictly fixed or strictly variable they are mixed in nature let me illustrate the concept of a mixed cost with a very simple and clear example Butler's car wash has a contract for its water supply that provides a flat monthly fee of $1,000 per month plus three dollars for each thousand gallons of water that are used and so if we were to look at this in spreadsheet form in column a I'm showing the gallons that could be used in a particular month the column B is the variable cost that would be incurred for example on row nine we can see $2,100 that's 700,000 gallons so 700 times three dollars or 2100 would be the variable cost at that level of usage the fixed cost however is $1,000 at each level of usage and we have our total cost the accumulation of columns B and C here and I've also plotted that to show the total water cost starting at $1000 even if we use zero gallons and then it goes up in a linear fashion for the variable cost as the usage continues to increase along the horizontal axis oftentimes a cost is not clearly fixed or variable in nature as it was for a butlers car wash so we may need to do an analysis to separate the total cost into presumed fixed and variable components one way for doing this is the high-low method it involves several steps the first of which is to find the highest level of activity and the lowest level of activity and identify the cost for each of those levels of activity and see what the difference is between the high cost and low cost and see what the difference is in the volume between the high level in the low level and based on that we would calculate a variable cost per unit in other words we have so much change in volume and so much change in cost that suggests the variability rate the remaining amount in each case would be the fixed cost recognize that this method can be very imprecise if we have outliers or rug data points in other words if a High Point is way out of the norm or a low point is way out of the norm then our calculations could be suspect so let's see how this would work here I've got an example we've identified our usage our highest-level was eight hundred and fifty thousand gallons and our lowest level was three hundred forty thousand gallons a difference of five hundred and ten thousand gallons we compare that to our cost the highest cost was three thousand five hundred fifty dollars the lowest cost two thousand twenty dollars a difference of fifteen hundred and thirty dollars so very simply we've got a range of five hundred and ten thousand gallons in a cost range of one thousand five hundred thirty dollars based on that we can calculate a variable cost per unit of three dollars so we're adopting an assumption that our variable cost is three dollars per unit notice our total cost at the high level is three thousand five fifty and at the low level two thousand twenty of that our variable cost would be twenty-five hundred fifty that is eight hundred and fifty times three and our low cost would be a thousand twenty that is three hundred and forty times three the difference or the remaining amount is fixed cost and it's shown to be a thousand dollars in each of the two columns so here we would have identified a high and a low point to discern that our fixed cost was a thousand and our variable cost is three dollars per unit a more statistically valid method for cost behavior analysis is the method of least squares it's based on regression analysis recognize that a straight-line can be defined by the formula y equals a plus BX where a is the intercept which would infer our fixed cost component B is the slope of the line which infers our variable cost component and X is the position on the x-axis that is the volume level so the least-squares method then defines a line that 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 spreadsheet programs can reused for this analysis this contrasts with a scatter graph method an alternative method where points are simply plotted on a graph and a line is drawn through the graph to approximate these values and so let's look at how the least squares method would work in this particular case we have monthly data we have units and we have total costs so that's our data set we've run a regression analysis using the spreadsheet software to determine that the intercept is 138 thousand 533 in the slope is ten point three four this suggests that for this business for this cost for this business that the fixed cost is a hundred and thirty eight thousand dollars and the variable cost is 10 dollars per unit now these values were derived from formulas included in the spreadsheet for example in cell b-17 I calculated the R square value which I'll comment more on in just a moment that's point seven nine eight the formulation in the spreadsheet are sq parens for the range of data C to the C thirteen regressed on the data b2 to be thirteen so that would be the formula for R square we would have a similar formulation within cell be fifteen and be sixteen for intercept and slope terms so let's look closer at the graph here if we notice the point that has an arrow drawn it appears that that's about ninety five thousand units on the horizontal axis and about $1,500,000 on the vertical axis that equates to the data point for December and if we had just done a scatter graph technique we would have simply drawn the dots on the graph and then drawn the line through the graph and see where it hits the y-axis and what the slope is as the line moves out and we could approximate the formula for the line there but what regression analysis does is it optimizes that line through those data points remember it's called regression analysis or least squares regression and so if we look at this particular point and we looked at each of the similar points and found the horizontal distance between the point and the line the sum of the squared distances would be minimized with regression analysis in other words that's deemed to be the best fit line through those data points let's finally close by thinking about that r-squared value the r-squared value of the least squares line is a statistical calculation that characterizes how well the line fits to a particular set of data in our example we saw an r-squared value of 0.7 9 8 that simply means that almost 80% of the variation can be explained by volume fluctuations the outliers are fairly small or in other words the points are fairly tightly clustered to align as a generalization the higher the r-squared is the closer it is to 1 the better fit is the line to the data set if the R square value was exactly 1 that would mean there is no variation between the dots and the line the line would pass exactly through each of the dots precisely if the r-squared value was very small 0.2 that would suggest that the line is not explaining a lot of the variation there is a lot of deviation between the the points and the line that r-squared finds as the best fit line