February 1996 € Volume 23 € No. 1

Budget For Planning and Control

An integral part of the modern business enterprise, budgeting not only aids in the planning process, but it also provides an array of accounting measures that can be used to hold managers accountable for the firm's performance.

By Richard Sansing

A budget is a projected set of consequences of carrying out planned activity. Firms use budgets to facilitate the communication of specialized information from throughout the firm so that an internally consistent production plan can be devised. The budgeted numbers are then used to record certain transactions. Differences between budgeted and actual performance then appear in the accounting records, and can be analyzed so as to evaluate the performance of the firm.

The budgeting process interacts with the operations research process in two ways. First, the budget process facilitates the transfer of both accounting and non-accounting information to those involved in operations. This information provides a basis for the formulation of the firm's production plan. Second, the budget reflects the production plan, and becomes a benchmark for subsequent performance evaluation. An analysis of deviations from the budget provides additional information that can be used when formulating the next period's production plan.

The Planning Stage
Feldman Toy Company makes two types of toys, regular and deluxe. Each toy requires the use of machine time in the production process. To illustrate the way the budget process works, consider the machinery department in Feldman. First, the department develops a flexible budget. A flexible budget for the machinery department is a prediction of that department's expenses during the accounting period as a function of its level of activity. By analyzing prior results, the department forecasts the relationship between its costs and activity level. For example, the department may use linear regression analysis to identify the relationship between costs and activity levels. An activity that is highly correlated with costs is sometimes referred to as a cost driver. Suppose monthly department costs vary with the number of machine hours (M) used during the month in the following manner. (1) Department costs = $60,000 + $15M The slope term reflects the cost of an additional machine hour, often referred to as the marginal cost of machine time. It is tempting, but imprecise, to refer to the intercept term as the department's fixed cost. If the true relationship between department costs and machine hours is nonlinear, e.g., if marginal costs are increasing, the intercept term will reflect both the fixed costs (department costs when machine hours are zero) as well as the nonlinearities in the cost function. For example, suppose the true relationship was: (2) Department costs = $68,000 + $7M + .002M2 If monthly machine usage was 2,000 hours per month, true total costs would be $90,000 and the marginal cost of machine time would be $15. A linear regression would produce an equation like that in (1); the total and marginal costs would be correct, but the intercept would not be a good approximation of the true fixed costs. The equation in (1) is sometimes referred to as a local linear approximation (LLA) of the firm's cost curve.

In addition to the flexible budget, the machinery department provides an estimate of machine time usage for each product as well as an estimate of total capacity for the month. Suppose the department estimates that the regular toy uses four minutes of machine time and the deluxe toy uses eight minutes of machine time. These estimates, or standards, may reflect average efficiency, ideal efficiency, or something in between. The department also estimates available machine time for the month to be 2,000 hours. The production plan would reflect the marginal cost of machine time to be $1 per unit for the regular toy (4 minutes @$15 per hour) and $2 per unit for the deluxe toy (8 minutes @$15 per hour). It would also reflect the capacity constraint shown in (3). (3) 4r + 8d < 120,000 The Production Stage
After accumulating information from throughout the firm, a production plan is chosen. Suppose this month's production calls for 10,000 of each type of toy. The budgeted numbers now become the basis of the firm's standard costing system. Under this system, department costs are assigned to products based on the standards reflected in the budget. Unlike the planning stage, which only used the marginal costs of the machinery department, the assignment of costs during the production stage should reflect all the costs of the department. This is called full absorption costing. Therefore, the intercept of (1) should be assigned to products.

Because the department expects to use 120,000 minutes of machine time, it allocates $.50 for each minute used, so that the intercept is "absorbed" into inventory. It allocates the marginal cost of $0.25 per minute to inventory as well. To simplify the accounting process and prepare for the creation of evaluation measures, the department records actual costs incurred in a temporary account, but assigns costs to products based on standard, not actual, usage. Therefore, $3 of department costs are assigned to each regular toy produced (four minutes @ $0.75 per minute), and $6 of department costs are assigned to each deluxe toy produced (eight minutes @ $0.75 per minute).

Suppose during the month the department actually incurs costs of $85,000. It worked on 11,000 regular toys and 9,000 deluxe toys. Total machine time was 118,000 minutes. How well did the department do, and why?

First, consider how the transactions were recorded during the month. The department accumulated the $85,000 costs incurred in an overhead account. It then allocated $3 as each regular toy was produced, and $6 as each deluxe toy was produced. This left a credit balance of $2,000 in the overhead account, which is closed to income at the end of the month. This balance, or variance, can be decomposed into three distinct variances: the spending variance, the efficiency variance, and the volume variance.

The spending variance is the difference between actual costs incurred and what would have been budgeted had the level of the cost driver been known in advance. Using (1), the budget would have been $60,000 + ($0.25 x 118,000) = $89,500. Therefore, there is a favorable spending variance of $4,500; costs were $4,500 lower than what we would have expected based on prior experience, given that level of the cost driver.

The efficiency variance is the difference between what would have been budgeted given actual activity and what would have been budgeted given actual output at standard usage. We would have expected to use total machine time of [(11,000 x 4) + (9,000 x 8)] = 116,000 minutes, given actual production of 11,000 regular toys and 9,000 deluxe toys. At standard usage, we would have budgeted overhead costs of $60,000 + ($0.25 x 116,000) = $89,000. Therefore, there is an unfavorable efficiency variance of $500. The efficiency variance reflects the difference between actual and expected machine usage, given output, multiplied by the marginal cost of machine time.

Finally, the volume variance is the difference between what would have been budgeted at standard usage and what was actually assigned to products. Since $89,000 would have been budgeted, but only $87,000 was assigned to products, we have an unfavorable volume variance of $2,000. This represents the difference between the 116,000 of standard usage and 120,000 of capacity, multiplied by the $0.50 rate at which the intercept of (1) is assigned to products. Note that the volume variance does not represent the opportunity cost of unused capacity.

Summing the three variances together yields a favorable variance of $2,000, the balance in the overhead account. The variances are summarized in Figure 1. The analysis of the variance suggests we paid less than usual for the items that go into overhead, used more machine time than our standards suggest, and had unused capacity.

Figure 1

The Evaluation Stage
These cost variances can be helpful in evaluating the performance of those responsible for them. The controllability principle states that managers should only be evaluated based on those measures that they can control. However, this principle is often misinterpreted. Suppose the machinery department production foreman is either competent or incompetent. Consider four possible outcomes of efficiency and volume overhead variances: both favorable (FF), favorable efficiency and unfavorable volume (FU), unfavorable efficiency and favorable volume (UF), and both unfavorable (UU). Prior experience suggests the probabilities of each type of foreman and each combination of variances is shown in Figure 2.

Figure 2

Casual application of the controllability principle suggests the foreman should be held responsible for efficiency variances, but not volume variances; competent managers are more likely than incompetent managers to get a favorable efficiency variance, but are just as likely to get a favorable volume variance. However, conditioned on the efficiency variance, the volume variance is informative regarding the foreman's competence. Suppose your prior belief is that the manager is competent with probability 50 percent. Upon seeing both favorable variances, you update your beliefs using Bayes' rule so that the probability that the manager is competent is 75 percent. If you see a favorable efficiency and unfavorable volume variance, however, the probability the manager is competent is only two-thirds.

Conclusion
Budgeting is a integral part of the modern business enterprise. It is a useful communication device for planning purposes, and provides an array of accounting measures that can be used to hold managers accountable for the firm's performance.

Two recommended sources for a more thorough discussion of these issues are "Managerial Uses of Accounting Information" by Joel Demski (Kluwer Academic Publishers) and "Accounting for Decision Making and Control" by Jerold Zimmerman (Irwin).

NOTE: To go to main feature article, "Why Are Public Budgets Such a Mess?" click here.

Richard Sansing is an associate professor of accounting at the Yale School of Management, where he teaches courses in taxation and management accounting. Professor Sansing's recent research has focused on transfer pricing, the effect of taxes on foreign investment decisions, and the usefulness of financial accounting measures of corporate income tax liabilities. He has a Ph.D. from the University of Texas at Austin.

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