An alternative vertical approach to analyzing overhead variances.

Little, Philip ; Saubert, Lynn K.

INTRODUCTION

Variance analysis has traditionally been among the more difficult topics for cost and managerial students to comprehend. Various methods have been suggested for presenting this material in a manner that will simplify calculations and facilitate an understanding of the resulting variances. Among these methods the most commonly used are the formula approach and the horizontal diagram approach, both of which are illustrated in many textbooks. Alternative approaches include a "common sense" approach (Chow, 1988), a graphic approach (Martin & Laughlin, 1988), and a vertical approach (Smith, 1991). While the techniques may vary, all of the methods attempt to simplify the calculations of the variances and promote an understanding and appreciation of the meaning of the resultant numbers.

The purpose of this article is to present an alternative model which builds on Smith's (1991) vertical model for analyzing overhead variances. First, the four basic components of our vertical model which comprise combinations of actual and standard costs of production are explained. Next, our vertical format for calculating manufacturing overhead variances using the four components is presented. Finally, an example is included to illustrate the applicability of our model for analyzing overhead variances.

Our vertical model for analyzing overhead presented in this paper should enhance students' understanding and learning in calculating two-way, three-way and four-way overhead variances. For comparison purposes, a review of other approaches is provided in the next section.

OTHER APPROACHES TO OVERHEAD VARIANCE ANALYSIS

Several approaches have been suggested to enhance the classroom presentation of variance analysis and enable students to more readily comprehend the concepts and calculations covered. Chow (1988) advocated a "common sense" approach which presented a written explanation of the variances. This approach, to be used to reinforce the traditional approaches, was designed to enhance the student's understanding of the underlying reasoning behind the variances. Referred to as a non-formula approach, the article consists of a series of formulas, using words instead of numbers.

A graphic approach to variance analysis was developed by Martin and Laughlin (1988). Using a series of overhead transparencies which present a logical progression of the development of the variances, students are provided a visual graphic illustration of the components of the variances. This method is also intended to supplement the traditional formula and diagram approaches.

An alternative format for presenting variance calculations, referred to as the "Vertical Method," was developed by Smith (1991). In this model fixed and variable overhead computations are integrated into a single formula, which, according to Smith, facilitates the preparation of journal entries as well as the calculation of the variances. Two features of this study are relevant to our article. First, by referring to educational psychology literature on learning organizers and learning transfer, he provided theoretical support for his vertical model to assist in organizing learning (pg. 81). Second, a classroom experiment, which tested the effectiveness of the traditional horizontal versus his vertical instructional approach indicated students in the vertical section scored significantly higher on variance exam questions than did the students in the horizontal sections even after controlling for grade point average factors. These results support the development of models which enhance students' understanding and comprehension of difficult academic topics. While the basic initial feature of our model is similar to Smith's vertical model, we extend the framework to provide a structural means of organizing, calculating and identifying the nature of the variance.

Similar to the alternative approaches discussed, we do not advocate rote memorization of formulas and computations. Like these other approaches, our model provides a pedagogical means by which students can organize and structure the data for analyzing overhead variances. Our model can then be used to develop an underlying understanding and appreciation of variances and standard costing.

THE MODEL

The model presented herein is based on a framework for organizing four combinations of actual and standard factory overhead costs. The components of the four data points in this framework are presented in Exhibit 1. The first data point is the total actual overhead costs incurred during the period. To compute the second data point both components use the standard overhead rates with variable overhead budgeted based on actual inputs and fixed overhead budgeted based on the denominator input. As with the flexible budget of the second data point, both components of the third data point are based on standard rates. However, variable costs are based on standard allowable inputs for actual output, while fixed overhead is again budgeted at the denominator level. The fourth data point, applied overhead, is determined by multiplying the standard allowable inputs for actual production times the standard rate for both variable and fixed overhead costs. Consistent with the horizontal analysis this framework for organizing the overhead data flows from the actual to the flexible budget to the standard applied overhead costs of production.

After organizing the overhead data into the four components, our vertical model utilizes the four data points to calculate the overhead variances in a systematic fashion. The model as shown in Exhibit 2 evolves from the two-way to three-way to four-way variance analysis.

SPECIAL FEATURES OF THE MODEL

There are three basic features of our vertical model for analyzing and computing overhead variances which represent an improvement over other similar models which are as follows:

(1) The variances are easily calculated from the four data points using a highly structured approach.

(2) The nature of the variances, whether unfavorable or favorable, can be easily determined.

(3) The relationships between the two-way, three-way, and four-way analysis are clearly identified.

Each of these features are illustrated in the following discussion based on the model framework as depicted in Exhibits 1 and 2.

In a two-way analysis the overhead variance is divided into two components, the flexible budget and volume variances. The flexible budget variance is defined as the difference between actual costs and budgeted costs for standard allowable inputs. In our model this variance is computed by subtracting data points #1 and #3. Accordingly, this variance is a combination of both spending and efficiency which will be broken down in the three-way analysis. The volume variance, related only to fixed overhead, is measured as the difference between the denominator volume input and standard input allowed times the standard rate for fixed overhead. In our model this variance is calculated by subtracting data points #3 and #4. Two factors should be noted concerning the volume variance. First, although data points #3 and #4 include a variable overhead component, it is the same for both points. Accordingly, the difference (volume variance) is caused solely by the fixed overhead component. Secondly, the volume variance (#3 - #4) is presented as the last variance calculated in all three systems. It is important to note that data point #2, the flexible budget for actual inputs, is not used in the two-way analysis of variance.

When calculating the three-way variance analysis the flexible budget variance is split between the spending variance and the efficiency variance. The two-way flexible budget variance, calculated as #1 minus #3, now incorporates data point #2. Accordingly, the variance is separated into the spending variance, #1 minus #2 and the efficiency variance, #2 minus #3. As will be demonstrated in the four-way analysis, the spending variance comprises two differences, one for variable overhead and one for fixed overhead. However, the spending variance in the three-way analysis is the difference between total actual overhead and the total flexible budget based on actual inputs. To complete the flexible budget variance from the twoway analysis, the next step is simply to subtract data points #2 and #3 to obtain a measure of efficiency. The volume variance in the three-way analysis is the same as in the two-way analysis.

In the four-way variance analysis, the spending variance is simply broken down into its variable and fixed components. The spending variance of the three-way system is now separated into a variable overhead spending variance and a fixed overhead spending variance. Consistent with the three-way analysis, the spending variances are calculated by subtracting data points #1 and #2. The efficiency variance and volume variance are calculated the same as before.

Our model provides an easy method for determining whether the variances are unfavorable or favorable. From Exhibit 2 it can be seen that the data point on the left in the variance computation represents unfavorable while the data point on the right represents favorable. Accordingly, whichever value is greater (i.e., the left side or right side) determines whether the variance is unfavorable or favorable. This method for determining the nature of the variance is consistent throughout the three different breakdowns of variance analysis.

ILLUSTRATIVE EXAMPLE

A hypothetical case will illustrate the methodology of our model.

ILLUSTRATIVE EXAMPLE
A hypothetical case will illustrate the methodology of our model.

Based on a standard volume of output of 4,000 units per month, the
standard overhead cost of the product manufactured by High Tech
Company consists of:

Variable Overhead (6 machine $ 48 per unit
 hours @ $8 per hour)
Fixed Overhead (6 machine $ 90 per unit
 hours @ $15 per hour)

During the current period of total of 4,400 units were
produced with the following costs:

Variable Overhead $245,000
Fixed Overhead $373,000
Actual Machine Hours were: 28,400 hours

Using the standard costs per unit and the actual costs
incurred in producing the output for the period, we can
develop the four data points of our framework.

1) Actual Overhead: Variable $245,000
Fixed $373,000 $618,000

2)Flexible Budget Based on Actual Inputs
Variable 28,400 hrs x 8 = $227,200
Fixed:Denominator Inputs $360,000 $587,200
 x Std Rate (4,000 x
 6 hrs) x 15 =

3) Flexible Budget Based on Standard Inputs Allowed:
Variable (4,400 x 6 hrs) x 8 = $211,200
Fixed 24,000 hrs x 15 = $360,000 $571,200

4) Applied Overhead:
Variable 26,400 hrs x 8 = $211,200
Fixed 26,400 hrs x 15 = $396,000 $607,200

Having combined the variable and fixed overhead data
into the four factors, we will now utilize these
combinations in the model to develop the respective
variances. Starting with a two-way analysis, we find:

Overhead Analysis:

Two-Way Analysis: Flexible Budget Variance

 Volume Variance

Three-Way Analysis: Spending Variance

 Efficiency Variance

 Volume Variance

Four-Way Analysis: Variable Overhead:
 Spending Variance

 Efficiency Variance

 Fixed Overhead:
 Spending Variance

 Volume Variance

Overhead Analysis: U - F

Two-Way Analysis: #1 - #3
 $618,000 - 571,200 = $46,800 U
 #3 - #4
 $571,200 - 607,200 = $36,000 F
Three-Way Analysis: #1 - #2
 $618,000 - 587,200 = $30,800 U
 #2 - #3
 $587,200 - 571,200 = $16,000 U
 #3 - #4
 $571,200 - 607,200 = #36,000 F
Four-Way Analysis:
 #1 - #2
 $245,000 - 227,200 = $17,800 U
 #2 - #3
 $227,200 - 211,200 = $16,000 U

 #1 - #2
 $373,000 - 360,000 = $13,000 U
 #3 - #4
 $360,000 - 396,000 = $36,000 F

This example illustrates the logical schematic approach of our system. Students can easily remember the numerical sequence of the model. Using the numbers of the data points, the two-way analysis sequence is 1-3, 3-4, noting that "2" is omitted from the two-way analysis. All data point numbers are included in the three-way analysis, using the system 1-2, 2-3, 3-4. Splitting he overhead into variable and fixed components, the four-way analysis system is 1-2, 2-3 for variable overhead and 1-2, 3-4 for fixed overhead. It should be noted that the volume variance, 3-4, is included in all systems, while the flexible budget variance of 1-3 is divided into component parts 1-2, 2-3 in the three- and four-way analysis.

Further, this example illustrates how our model allows students to easily determine the nature of the variances. If the first number of the sequence is larger than the second, the variance is unfavorable. This is logical since the cost related to the data points are organized from actual to applied numbers. Since the data points are ordered to measure actual, flexible budget based on actual inputs, flexible budget based on standard inputs allowed, and finally applied overhead costs, if the first number of the difference exceeds the second number the difference should be unfavorable. Likewise, if the first number which represents the actual or allowable costs is less than the second number representing another allowable or applied overhead cost, the variance should be favorable.

SUMMARY AND CONCLUSIONS

Overhead variance analysis is a difficult topic for students to understand. The various formulas and calculations for the individual variances are hard to comprehend and remember. Our model presented in this article provides a framework to organize the overhead cost components and a structured approach to calculate the variances. The favorable or unfavorable nature of the variance is easily determined in this system. Using this model as a learning organizer, an understanding of the components of the data as well as the computations of the variances is facilitated.

REFERENCES

Chow, C. W. (1988, Spring). A common sense approach to teaching variance analysis. The Accounting Educators' Journal, 42-48.

Martin, J. R., & Laughlin, E. J. (1988, Fall). A graphic approach to variance analysis emphasizes concepts rather than mechanics. Issues in Accounting Education, 351-364.

Smith, K. J. (1991, Winter). An alternative method of variance analysis instruction. The Accounting Educators' Journal, 75-94.

Philip Little, Western Carolina University

Lynn K. Saubert, Radford University

Exhibit 1
Framework for Analyzing Variable and Fixed Factory Overhead Variances

1. Actual Overhead

Variable: Actual Inputs X Actual Rate
Fixed: Actual Inputs X Actual Rate

2. Flexible Budget Based on Actual Inputs

Variable: Actual Inputs X Standard Rate
Fixed: Budgeted Overhead: Denominator Inputs X Standard Rate

3. Flexible Budget Based on Standard Inputs Allowed

Variable: Standard Inputs X Standard Rate
Fixed: Budgeted Overhead: Denominator Inputs X Standard Rate

4. Applied Overhead

Variable: Standard Inputs X Standard Rate
Fixed: Standard Inputs X Standard Rate

Exhibit 2
Model for Vertical Variance Analysis

Two-Way Analysis U - F
 Flexible Budget Variance: 1 - 3
 Volume Variance: 3 - 4
Three-Way Analysis
 Spending Variance: 1 - 2
 Efficiency Variance: 2 - 3
 Volume Variance: 3 - 4
Four-Way Analysis
 Variable Overhead:
 Spending: 1 - 2
 Efficiency: 2 - 3
 Fixed Overhead:
 Spending: 1 - 2
 Volume: 3 - 4

Spending: (Actual Rate - Standard Rate) X Actual Inputs
Variable Overhead Efficiency: (Actual Inputs - Standard
Inputs) X Standard Rate
Fixed Overheard Volume: (Denominator Inputs - Standard
Inputs) X Standard Rate