Examples of Cost and Output Relationships from Real Companies

Updated January 02, 2003

Regression Analysis and Cost Behavior

Regression analysis is often used to study cost-output relationships to make inferences about cost behavior.  The simpliest application is with XY plots of data overlaid with a fitted least squares line.  However, using real data with regression analysis can create problems if the person doing the analysis does not watch for problems with the data.

The following graphs of cost and output have been prepared from real company data to illustrate some problems accountants encounter when analyzing cost-output relationships. In all these graphs the horizontal axis represents output, and the vertical axis represents cost.

Matching Data to the Same Time Period

The first graph shows units produced in a bag manufacturing facility that pays workers a fixed amount per bag sewn. Notice how the data do not fall directly on the plotted line as one would expect. This probably occurs because the company records labor cost monthly, but the production personnel record units produced weekly. In other words, the production people and the accountants do not use the same time period for reporting data.

The next graph shows a plot of total cost transferred to finished goods and the number of units produced. Again, one would expect the plotted points to fall neatly on the plotted line. If the production personnel track units produced by week and the accountants record movement for the month, the two groups have incompatible time periods.

Erroneous Data Reported

Actual hours used to pay workers and the time these workers reported they worked on various jobs appear next. There should be a very close correlation between the hours generated by a time clock and the time workers report they spend working on jobs, but the graph indicates otherwise. This company had a problem with its time reporting, but management had been unable to train workers to reliably record the amount of time spent on each job. The time clock told how many total hours employees worked each day, but the workers recorded the time they spent working on different jobs during the day on separate time sheets.

Clean and Reliable Data

Now for an example of clean and reliable data. Consider this graph of monthly rental cost and total shipments. It is not hard to determine that rent is a fixed cost for this company.

Another example of clean and reliable data appears next, but one does not get the results one would expect. The depreciation expense in this graph varies from month to month. Asset sales and acquisitions account for this jumpiness in depreciation expense, an expense almost all accountants call a fixed expense.

Output Measurement Problem

Output measurement can be a difficult issue in some companies. The company illustrated here puts enamel coatings on steel parts. These parts range in size from the side panel for a refrigerator to the drip pan for a barbeque grill. Consequently, this company measures output by the sales value of the units produced. It is not perfect, but you try to develop a better one.

Price Changes and Matching Costs to Time Periods

If an accountant tries to measure the cost-output relationship over a long time for a company, he or she may have problems because of price changes over time. Price indexes can help to adjust the data for these price changes, but the next graph illustrates a price change one cannot adjust this way. This graph shows the natural gas cost recorded monthly for a foundry that produces aluminum alloys. Total tons produced appears on the horizontal axis, and monthly expenditures on natural gas appear on the vertical axis. The company buys gas on the spot market, so the price varies from day to day. Also, the company records the gas cost when they get the bill, so the timing of the expenditure may be completely unrelated to when the company will use the gas.

Concluding Comments

These graphs illustrate some of the data problems accountants must consider when attempting to measure the relationship between output and cost. Your textbook and class discussion will highlight other problems. Always remember to ask if the results of your regression analysis of real world data makes sense.