Data Collection and Adjustment Issues

Learning Objective 7 Be aware of data problems encountered in estimating cost functions

• for example, unreliable data and poor recordkeeping, extreme observations, treating fixed costs as if they are variable, and a changing relationship between a cost driver and cost

The ideal database for estimating cost functions quantitatively has two characteristics:

1. THE DATABASE SHOULD CONTAIN NUMEROUS RELIABLY MEASURED OBSERVATIONS OF THE COST DRIVER (THE INDEPENDENT VARIABLE) AND THE RELATED COSTS (THE DEPENDENT VARIABLE). Errors in measuring the costs and the cost driver are serious. They result in inaccurate estimates of the effect of the cost driver on costs.
2. THE DATABASE SHOULD CONSIDER MANY VALUES SPANNING A WIDE RANGE FOR THE COST DRIVER. Using only a few values of the cost driver that are grouped closely together cause managers to consider too small a segment of the relevant range and reduces the accuracy of the estimates obtained.

Unfortunately, management accountants typically do not work with a database having both characteristics. This section outlines some frequently encountered data problems and steps to overcome these problems. Managers should ask about these problems and assess how they have been resolved before they rely on cost estimates generated from the data.

• THE TIME PERIOD FOR MEASURING THE DEPENDENT VARIABLE DOES NOT PROPERLY MATCH THE PERIOD FOR MEASURING THE COST DRIVER. This problem often arises when a company does not keep accounting records on the accrual basis. Consider a cost function for a transportation company with engine-lubricant costs as the dependent variable and the number of truck-hours as the cost driver. Assume that the lubricant is purchased sporadically and stored for later use. Records maintained on the basis of lubricants purchased will indicate small lubricant costs in many months and large lubricant costs in a few months. These records present an inaccurate picture of the relationship between the cost driver and costs. The analyst should use accrual accounting to measure the cost of lubricants consumed to better match these costs with the truck-hours cost driver in this example.
• FIXED COSTS ARE ALLOCATED AS IF THEY ARE VARIABLE. For example, costs such as depreciation, insurance, or rent may be allocated to products to calculate the cost per unit of output. The danger for managers is to regard these costs as variable rather than as fixed. The costs appear to be variable because of the allocation methods used, not the actual behavior of costs. To avoid this problem, the analyst should carefully distinguish fixed costs from variable costs and not treat allocated fixed cost per unit as a variable cost.
• DATA ARE EITHER NOT AVAILABLE FOR ALL OBSERVATIONS OR ARE NOT UNIFORMLY RELIABLE. Missing cost observations often arise because data have been entered manually rather than electronically and are not recorded or classified correctly. For example, a firm’s marketing costs may be understated because the costs of sales visits to customers may be incorrectly recorded as customer-service costs. Errors also arise when data on cost drivers originate outside the internal accounting system. For example, the accounting department may obtain data on testing-hours for medical instruments from the company’s manufacturing department and on number of items shipped from the distribution department. One or both of these departments might not be focused on keeping accurate records. To minimize these problems, the cost analyst should design data collection reports that regularly and routinely obtain the required data and follow up immediately whenever data are missing.
• EXTREME VALUES OF OBSERVATIONS OCCUR. These values arise from (1) errors in recording costs (for example, a misplaced decimal point), (2) nonrepresentative periods (for example, from a period in which a major machine breakdown occurred), or (3) observations outside the relevant range. Analysts should adjust or eliminate unusual observations before estimating a cost relationship.
• THERE IS NO HOMOGENEOUS RELATIONSHIP BETWEEN THE COST DRIVER AND THE INDIVIDUAL COST ITEMS IN THE DEPENDENT VARIABLE-COST POOL. A homogeneous relationship exists when each activity whose costs are included in the dependent variable has the same cost driver. In this case, a single cost function can be estimated. As discussed in Step 2 for estimating a cost function using quantitative analysis (see Estimating a Cost Function Using Quantitative Analysis), when the cost driver for each activity is different, separate cost functions (each with its own cost driver) should be estimated for each activity. Alternatively, as discussed in section Multiple Regression and Cost Hierarchies, the analyst should estimate the cost function with more than one independent variable using multiple regression.
• THE RELATIONSHIP BETWEEN THE COST DRIVER AND THE COST IS NOT STATIONARY. This occurs when the underlying process that generated the observations has not remained stable over time. For example, the relationship between number of machine-hours and manufacturing overhead costs is unlikely to be stationary when the data cover a period in which new technology was introduced. In this case, the analyst should split the sample into two parts and estimate separate cost relationships—one for the period before the technology was introduced and one for the period after the technology was introduced. If it turns out that the estimated coefficients for the two periods are similar, the analyst can pool the data to estimate a single cost relationship. When feasible, pooling data provides a larger dataset for the estimation, which increases confidence in the cost predictions being made.
• INFLATION HAS AFFECTED COSTS, THE COST DRIVER, OR BOTH. For example, inflation may cause costs to change even when there is no change in the level of the cost driver. To study the underlying cause-and-effect relationship between the level of the cost driver and costs, the analyst should remove purely inflationary price effects from the data by dividing each cost by the price index on the date the cost was incurred.

In many cases, a cost analyst must expend considerable effort to reduce the effect of these problems before estimating a cost function on the basis of past data. Before making any decisions, a manager should carefully review any data that seem suspect and work closely with the company’s analysts and accountants to obtain and process the correct and relevant information.