CONSTRUCTION LABOR VARIANCE ANALYSIS TEACHING MODEL

INTRODUCTION

One of the major problems facing the construction industry today is the lack of trained manpower. Projections indicate that this problem will grow in the 1990's. The lack of trained manpower results in lower productivity. Since the labor cost report measures productivity and indicates where corrective action is needed, its importance will increase in the 1990's.

Traditional construction labor cost reports compare estimated labor costs to actual or forecasted labor costs. This comparison of costs is usually accompanied by a comparison of quantities, production rates, and/or unit prices. Rarely is the total variance broken down into the variances caused by each labor cost component (quantities, production rate, and wage rate). This lack of breakdown causes a problem - the user of the report has to use supplemental methods to determine which component(s) of labor costs is contributing the largest part of the variation between estimated and actual or forecasted costs. What is needed is an analysis method that calculates the dollar impact of the change in each. component of the total labor costs. One method to measure the individual impact of each change is to use the standard cost model from management accounting.

STANDARD COST MODEL

As used in management accounting, standard costs are budget unit costs (unit prices). By using the standard costs to calculate labor price (wage rate) and efficiency (production rate) variances, managers can better understand why actual costs are different than the standard costs and take the proper corrective action.

The labor price variance is the difference between the standard and actual labor price times the actual hours used to produce one unit of output. The efficiency variance is the difference between the standard and actual hours used to produce one unit of output times the standard labor price. The calculation of the price and efficiency variances are shown in equations 3 and 4 [2].

While most accounting theorists subscribe to the standard cost model described in equations 3 and 4, others believe that the price variance should be calculated using the standard hours instead of the actual hours. This creates a mixed or joint variance model as shown in equations 5, 6, and 7. The joint variance makes sense because it is created by both a change in prices and hours [1].

The standard cost model is used in construction to anal e the changes between the actual and budget unit prices for labor. It is useful to multiply the labor price (wage rate) and efficiency (production rate) variances by the quantity to get the magnitude of the variances in dollars.

In addition to differing unit prices, labor costs also vary according to differences between the actual and budget quantities. The quantity is the third component of labor costs. A standard cost model can be used to evaluate quantity and unit price variances. This model is shown in equations 8, 9, and 10. The quantity and unit price variance are expressed in dollars.

To fully examine a difference between the budget and actual costs requires two steps. In the first step, equations 8, 9, and 10 are used to determine the quantity and unit price variance. Then equations 5, 6, and 7 can be used to breakdown the unit price variance into wage rate and production rate variances.

This two step method was taught in the Construction Cost Control course in the Building Construction Department at Purdue. Over time a method evolved to breakdown a labor cost variance directly into its quantity, production rate, and wage rate components. This method is the construction labor variance model.

CONSTRUCTION LABOR VARIANCE MODEL

Figure 1 presents a construction labor variance analysis for one account for one reporting period. As can be seen, there are a number of calculations required. To help explain construction labor variance analysis in the course, a three dimensional color coded physical model is used. On the model the length, width, and height (x, y, and z axis) represent the quantity, production rate, and wage rate. The volume of the solid (length x width x height) represents the total labor cost. The impact on labor costs of changes in the quantity, production rate, and wage rate, either separately or in combination, are clearly shown by the model.

On the physical model each variance or joint variance has its own color coded volume. Putting all the variance and joint variance volumes together with the estimate volume gives the total actual or forecasted labor cost.

The construction labor variance analysis shown in Figure 1 has 75 bits of data. This analysis would require a major effort if it was done manually. However, a computerized spreadsheet is used so that only six pieces of data are required to be entered for each reporting period to calculate all the variances. Three pieces of data are required for the "actual this period" column: the quantity installed, the man-hours expended and the labor dollars paid. The "actual this period" data is added to last week's "actual to date" data to venerate the information for this week's "actual to date" column.

In order to forecast the costs for the account, management predicts the final quantity, wage rate and production rate. In Figure 1, it was assumed that the "actual to date" wage rate and production rate were the best predictors of the forecast wage rate and production rate. This assumption is not always true because the work remaining may be more or less difficult than the work completed. Therefore, management must use all information available to them to make their predictions.

The estimated quantity, wage rate and production rate must be entered only for the first analysis period. This data then remains constant throughout the project. All the other pieces of data from Figure 1 are calculated by the spreadsheet program. When using a spreadsheet program to calculate the changes between the estimate and the forecast it is important to subtract the forecast from the estimate. Negative values indicate that the forecast amount is greater than the estimate and will cause an unfavorable variance. The computer calculates the percent complete by dividing the actual to date quantity by the forecasted quantity.

The other calculations in Part 1 of Figure 1 are self-explanatory. However, the calculations in Part 2 need some explanation. The estimated (est.) total labor dollars is the product of the estimated quantity, the estimated wage rate and the estimated production rate, equation 11. The forecasted (F/C) total labor dollars is the product of the sum of the estimated quantity and the change in the estimated quantity, the sum of the estimated wage rate, and the change in the estimated wage rate, and the sum of the estimated production rate and the change in the estimated production rate, equation 12. The construction labor variance analysis separates and isolates the effect of each component. Favorable variances occur when the forecasted cost is less than the estimated cost.

The quantity variance is the product of the change in the quantity, the estimated wage rate, and the estimated production rate . The wage rate variance and the production rate variance are calculated in a similar manner, see equations 13, 14, and 15.

When two components of the total labor cost change at the same time there is a joint effect. The joint effect of the quantity and the wage rate changing at the same time is the product of the change in the estimated quantity, the change in the estimated wage rate, and the estimated production rate. The joint quantity-production rate and the joint wage rate-production rate variances are calculated in a similar manner, see equations 16, 17, and 18.

Empirical analysis has shown that there are three rules to determine if the joint variance is favorable or unfavorable. The first rule is that if both individual changes are favorable then the joint variance is unfavorable. The second rule is that if both individual changes are unfavorable then the joint variance is unfavorable. The third rule is that if one of the individual changes is favorable and the other individual change is unfavorable then the joint variance is favorable. When using a spreadsheet program these rules are incorporated by multiplying the joint variance calculation by (-1).

When all three components of the total labor cost change at the same time there is also a three-way joint variance. This variance is the product of the change in the estimated quantity, the change in the estimated wage rate, and the change in the estimated production rate, see equation 19.

 There are four rules to determine if the three way joint variance is favorable or unfavorable. However, unlike the two way joint variances, do not multiply the three way joint variance calculation by (-1). The first rule is that if all of the individual changes are favorable then the three way variance is favorable. The second rule is that if all of the individual changes are unfavorable then the three way ^joint variance is unfavorable. The third rule is that if one of the individual changes is favorable and the other two individual change are unfavorable then the joint variance is favorable. The fourth rule is that if one of the individual changes is unfavorable and the other two individual change are favorable then the joint variance is unfavorable.

 The calculations described thus far have broken down the change between the estimated and forecasted labor costs into seven variances. These variances and the formulas to calculate the magnitude of each variance are listed in Table 1. From Table 1 it can be seen that the sum of the estimate plus the variances is algebraically equal to the forecast.

 One problem with the construction labor variance analysis is that the seven variances and joint variances can confuse the overall analysis of the causes of cost overruns. One way to solve this problem is to prorate the joint variances to the main effect variances (quantity, wage rate and production rate) based on the magnitude of the main effect variances. This can be as done by the computer as shown in Figure 1. The adjusted variances can then be summarized in a report like the one presented in Figure 2 [3].

 Figure 2 is a summary of the accounts for a very simple project. Reviewing the variances in Figure 2 identifies trends in the variances. In this example there is a pattern of unfavorable production rate variances for the accounts employing masons (accounts 04250 and 04370). In addition to highlighting trends in quantities, wage rates, and production rates, the summary variance report is useful in identifying accounts that have a favorable total variance, but also have one or two components with unfavorable variances. Relying only on total variances will cause management to overlook opportunities for cost saving measures. Management needs to take corrective action whenever any component is predicted to have an unfavorable variance. An example of this situation is shown in account 06150 in Figure 2. In this account the total variance is favorable, but the quantity variance is unfavorable and management needs to look for the reasons why.

 The summary variance report not only identifies the accounts with unfavorable variances, but it also measures the magnitude of these variances. These magnitudes can be used to prioritize the accounts needing management's attention. The summary variance report is befitting to the management by exception philosophy.

CONCLUSION

The value of the construction labor variance analysis is that it provides more useful information to managers about cost variances than the standard cost model or the traditional labor cost analysis, but it does not require any more inputs or time to prepare. The variance analysis labor cost analysis uses the same inputs (quantities, man-hours, and labor dollars) as the traditional labor cost analysis. Teaching the construction labor variance analysis is aided by the use of the three dimensional color coded physical model.

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