Let's look now at the high-low method of estimating a cost equation. With the high-low method, you use past cost and activity data just as you do with scatter plots. But you want to ensure that you have observations from a typical or representative low-activity period and a typical or representative high-activity period. So how do you do that? Let's look at this scatter plot of data on cost in units. You'll see that there are many observations, almost all of which are grouped together. But there are two observations that are outliers. To use the high-low method, the first step is we need to pick a typical high and typical low-activity observation. Now, while this observation is a low-activity observations because it's a low number of units, it would not be considered typical or representative, so we would not want to choose it for our high-low estimation. And likewise, we would not want to choose the other outlier as our high-activity observation. Let me suggest we choose this one, it looks pretty typical down in the low-activity area. And let's choose this one. It looks pretty typical up in that high-activity level. Okay, this one is a cost of 60,000 at 5,000 units. And this is a cost of 100,000 at 15,000 units. Okay, so we have our high and low-activity observations. Now, think about this. Assuming fixed cost are the same at each of these two points, any change in cost from one point to the other would be due solely to variable cost. So here's what we do. Step 2, we find the variable cost per unit of activity by dividing the difference in cost, or the change in cost between the two points, by the difference in activity between the two points. Let's work that here. So we've got our high observation total cost of 100,000. And our low-activity cost of 60,000. And we have our high-activity units of 15,000 and our low-activity units of 5,000. So we see that cost go up $40,000 when the number of units goes up $10,000. So that would be a variable cost of $4 per unit, okay? Next, the third step, we find the fixed cost by subtracting the variable cost at either of these activity levels from the total costs at that level. Let's do that. We should be able to do this from either of the two observations. I'll just do it at the high-activity level observation. We'll do this at $100,000, okay? Total cost at our high-activity level observation. Our variable cost per unit are $4 per unit times the 15,000 units at our high-activity level. So our $100,000 minus our 60,000 in variable cost would give us fixed cost of $40,000. Okay? Now, we just as easily could have done this with the low-activity observation, and let me illustrate that one as well. The total cost at the low-activity level was $60,000 variable costs per unit of four. 5,000 units. 60,000 minus 20,000 gives us $40,000. So regardless of which one we use, we're still going to calculate fixed costs of $40,000. That makes sense, doesn't it? We would expect fixed cost to be the same between those two observations. Now, finally, I can use all these information to write the equation that will help us predict cost. Here, that equation would be Y is equal to 4. The slope of the line, or the variable cost per unit, times x the number of units plus fixed costs of $40,000. That's the high low method. Not bad. Now, you might recall that earlier, I mentioned the third approach to estimating cost functions. Least squares regression. Using least squares regression is beyond the scope of this course, but generally speaking, least squares regression is a statistical approach that fits a line to a set of data. So rather than eyeballing a line from a scatter plot using a straight edge, or calculating the equation of a line from just two data points using the high-low method, the least squares regression method uses a more sophisticated statistical approach to estimate the equation of a line. That takes into account all of the data points that are available.
