CHAPTER 1: Management Accounting Defined, Described, and Compared to Financial Accounting

MANAGEMENT ACCOUNTING CONCEPTS AND TECHNIQUES

By Dennis Caplan, University at Albany (State University of New York)

CHAPTER 17: Cost Variances for Variable and Fixed Overhead

Chapter Contents:

- Cost variances for variable overhead

- Cost variances for fixed overhead

- The fixed overhead spending variance

- The fixed overhead volume variance

- Additional issues related to the volume variance

- Comprehensive example of fixed overhead variances

- Exercises and problems

Cost Variances for Variable Overhead:

The formulas for splitting the flexible budget variance for variable overhead into a “price” variance and an “efficiency” variance are the same as the formulas for direct materials and direct labor explained in Chapter 7. The “price” variance for variable overhead is called the variable overhead spending variance:

Spending variance = PV = AQ x (AP – SP)

Efficiency variance = EV = SP x (AQ – SQ)

Where AP is the actual overhead rate used to allocate variable overhead, and SP is the budgeted overhead rate. The “Q’s” refer to the quantity of the allocation base used to allocate variable overhead, so that AQ is the actual quantity of the allocation base used during the period, and SQ is the standard quantity of the allocation base. The standard quantity of the allocation base is the amount of the allocation base that should have been used (i.e., would have been budgeted) for the actual output units produced.

Given the use of the allocation base in these formulas for the cost variances for variable overhead, the meaning of these variances differs fundamentally from the interpretation of the variances for direct materials and direct labor. Consider a company that allocates electricity using direct labor as the allocation base. A negative variable overhead efficiency variance does not necessarily mean that the factory used more electricity than the flexible budget quantity of kilowatt hours for the actual outputs produced. Rather, the negative variance literally means that the factory used more direct labor than the flexible budget quantity for direct labor. If there is a cause-and-effect relationship between the allocation base and the variable overhead cost category (i.e., if more direct labor hours implies more electricity used), then the negative efficiency variance suggests that more electricity was used than the flexible budget quantity, but the efficiency variance does not measure kilowatts directly.

Similarly, a negative spending variance for variable overhead does not necessarily mean that the cost per kilowatt-hour was higher than budgeted. Rather, a negative spending variance for variable overhead literally states that the actual overhead rate was higher than the budgeted overhead rate, which could be due either to a higher cost per kilowatt-hour, or more kilowatt hours used per unit of the allocation base. Hence, what one might think should be included in the efficiency variance (kilowatt hours required per direct-labor-hour being higher or lower than budgeted) actually gets included as part of the spending variance.

Cost Variances for Fixed Overhead:

Whereas the cost variances for direct materials, direct labor, and variable overhead all use the same two formulas, the cost variances for fixed overhead are different, and do not use these formulas at all.

Also, whereas cost variances for direct materials, direct labor, and variable overhead can be calculated for individual products in a multi-product factory, cost variances for fixed overhead can only be calculated for the factory or facility as a whole. (More precisely, fixed overhead cost variances can only be calculated for the combined operations to which the resources represented by the fixed costs apply.)

There are two fixed overhead cost variances: the spending variance and the volume variance.

The Fixed Overhead Spending Variance:

The fixed overhead spending variance is the difference between two lump sums:

Actual fixed overhead costs incurred - Budgeted fixed overhead costs

The fixed overhead spending variance is also called the fixed overhead price variance or the fixed overhead budget variance.

The Fixed Overhead Volume Variance:

The fixed overhead volume variance is also called the production volume variance, because this variance is a function of production volume. The volume variance attaches a dollar amount to the difference between two production levels. The first production level is the actual output for the period. The second production level is the denominator-level concept in the budgeted fixed overhead rate, expressed in units. As discussed in the previous chapter, there are two common choices for this denominator:

(1) budgeted production

(2) factory capacity

The interpretation of the volume variance depends on which of these two denominators are used, but in either case, the production volume variance is the difference between budgeted fixed overhead (a lump sum), and the amount of fixed overhead that would be allocated to production under a standard costing system using this fixed overhead rate.

The volume variance with budgeted production in the denominator of the O/H rate:

First we use budgeted production to calculate the volume variance. In this case:

volume variance

= (

budgeted fixed overhead

units produced

) -

budgeted fixed overhead

budgeted production

The term in parenthesis equals the amount of fixed overhead that would be allocated to production under a standard costing system, when budgeted production is the denominator-level concept.

Since

budgeted fixed overhead ÷ budgeted production = budgeted overhead rate

the above expression for the volume variance is algebraically equivalent to the following formula:

volume variance

(units produced - budgeted production) x budgeted overhead rate

This formula for the volume variance illustrates the statement above; that the volume variance attaches a dollar amount to the difference between two production levels. In this case, the two production levels are actual production and budgeted production. The interpretation of the volume variance, when budgeted production is used in the denominator of the overhead rate, is the following. When actual production is less than budgeted production, the volume variance represents the fixed overhead costs that are not allocated to product because actual production is below budget. In this case, the volume variance is unfavorable. When actual production is greater than budgeted production, then the volume variance represents the additional fixed overhead costs that are allocated to product because actual production exceeds budget. In this case, the volume variance is favorable.

The intuition for when the volume variance is favorable and when it is unfavorable is the following. If the company can produce more units of output using the same fixed assets (i.e., the resources that comprise fixed overhead), then assuming those additional units can be sold, the company is more profitable. When fixed overhead is allocated to production, this greater profitability is reflected in a lower per-unit production cost, because the same amount of total fixed overhead is spread over more units. On the other hand, if fewer units are produced than planned, then the same fixed overhead is spread over fewer units, the per-unit production cost is higher, and the company is less profitable. This higher or lower profitability that arises from changes in production levels is not an artifact of the accounting system. Even if the company uses Variable Costing, and expenses fixed overhead as a lump-sum period cost, when the company makes and sells fewer units than planned using the same fixed overhead resources, it really is less profitable than was budgeted, and when the company makes and sells more units than planned using the same fixed overhead resources, it really is more profitable than was budgeted.

The volume variance with factory capacity in the denominator of the O/H rate:

Next we use factory capacity to calculate the volume variance. In this case:

volume variance

= (

budgeted fixed overhead

units produced

) -

budgeted fixed overhead

factory capacity

Since

budgeted fixed overhead ÷ factory capacity = budgeted overhead rate

the above expression for the volume variance is algebraically equivalent to the following formula:

volume variance

(units produced - factory capacity) x budgeted overhead rate

The interpretation of the volume variance, when factory capacity is used in the denominator of the overhead rate, is the following. Actual production is almost always below capacity. The volume variance represents the fixed overhead costs that are not allocated to product because actual production is below capacity. Hence the volume variance represents the cost of idle capacity, and this variance is typically unfavorable. For this reason, this volume variance is sometimes called the idle capacity variance. In the unlikely event that the factory produces above capacity (which can occur if the concept of practical capacity is used, and actual down-time for routine maintenance, etc., is less than expected), then the volume variance represents the additional fixed overhead costs that are allocated to product because actual production exceeds capacity. In this case, the volume variance is favorable.

Additional Issues Related to the Volume Variance:

Under what circumstances would a company calculate the volume variance using budgeted production as the denominator-level concept, and under what circumstances would a company use factory capacity as the denominator-level concept?

The use of budgeted production in the calculation of the volume variance attaches a lump sum benefit or cost to actual production levels that exceed or fall short of budgeted production levels. For this reason, many companies consider this calculation of the volume variance to be an important performance measure for the factory manager and marketing managers responsible for making and marketing the product.

The use of factory capacity in the calculation of the volume variance provides an indication of how low the per-unit cost can go, if demand equals or exceeds factory capacity. If senior management would like product managers to make pricing and operating decisions based on a long-term expectation that demand for the product will equal or exceed factory capacity, even though current or short-term demand is below capacity, calculating the per-unit cost in this manner will encourage product managers to take this long-run perspective. For example, consider the launch of a new product line in a new factory. If fixed overhead is allocated based on budgeted production, then product managers might feel pressured to set sales prices that will cover full product costs at initially-low production levels, but these sales prices might be too high to generate sufficient initial consumer interest in the product for a successful product launch.

Another reason to use factory capacity in the denominator of the fixed overhead rate, and in the calculation of the volume variance, is that doing so isolates the cost of idle capacity. Often, the decision to build a factory that is larger than current demand warrants is a strategic decision made at high levels within the organization. If the fixed overhead associated with this factory is allocated based on budgeted or actual production, the per-unit cost of every unit manufactured includes a small portion of the cost of this strategic decision, and the cost reports of factory managers and the product profitability statements of product managers are negatively affected by this unused capacity. Some companies prefer to isolate the cost associated with this strategic decision, and to either show the cost of idle capacity as separate line-items on the cost reports and profit statements of the factory manager and product managers, or remove this cost entirely from these performance reports, and report it only at the corporate level.

Allocating fixed overhead using actual production can provide managers short-run incentives to overproduce, because as production increases, the per-unit cost decreases. Similarly, calculating the volume variance using budgeted production in the denominator of the overhead rate can provide managers short-run incentives to overproduce, because as production exceeds budget, the volume variance becomes increasingly favorable. For this reason, some companies choose not to allocate fixed overhead at all. However, the use of factory capacity in the denominator of the fixed overhead rate accomplishes the same objective, because it isolates the volume variance such that the performance reports of these managers need not be affected by it.

We have assumed, throughout this section, that fixed overhead is allocated based on units of output. However, we saw in the chapter on activity-based costing that units of production is often a poor choice of allocation base in a multi-product factory, and many companies that use standard costing systems use allocation bases that are more sophisticated, such as direct labor hours or direct materials dollars. The question might arise, how does the use of a different allocation base, such as direct labor hours, affect the calculation of the volume variance? The answer is: Not at all. Because of the way in which standard costing systems work, the amount of fixed overhead that will be allocated to product does not depend on the choice of allocation base.

For example, assume that a one-product company budgets two direct labor hours to make each unit, and assume that if fixed overhead is allocated based on output units, the budgeted fixed overhead rate is $10 per unit. Then using direct labor hours as the allocation base, the budgeted fixed overhead rate is $5 per direct labor hour. Because of the mechanics of standard costing systems, no matter whether the $10-per-unit rate is used, or the $5-per-direct-labor-hour rate is used, $10 of fixed overhead will be allocated to every unit produced, no matter how many direct labor hours are actually used per unit. (If this fact is not obvious to you, refer back to Chapter 10 on standard costing.) Therefore, for the purpose of calculating the volume variance, we might as well use the easiest allocation base, which is units-of-output.

It is important to recognize that even though most manufacturing companies use a standard costing system, and even though the calculation of the fixed overhead volume variance relies on the concept of standard costing, companies can calculate the volume variance even if they do not use a standard costing system. In this case, the calculation is identical to the discussion above, but the company will not be able to obtain the required information from the cost accounting system itself, but rather, will need to make a separate calculation.

Comprehensive Example of Fixed Overhead Variances:

The Coachman Company makes pencils. The pencils are sold by the box. Following is information about the company’s only factory:

Budget

Actual

Capacity

Number of boxes

Direct labor hours

Machine hours

Fixed overhead

10,000

200

500

$40,000

12,000

250

650

$42,000

20,000

The outputs here are boxes of pencils. The inputs are direct labor hours and machine hours. First we calculate a fixed overhead rate using actual amounts, and output units as the allocation base:

$42,000 ÷ 12,000 boxes = $3.50 per box.

Using this overhead rate, every box of pencils is costed at the variable cost of production plus $3.50 in allocated fixed overhead.

Next: we calculate a fixed overhead rate using budgeted costs, and budgeted output units as the denominator-level concept:

$40,000 ÷ 10,000 boxes = $4.00 per box.

Next: we calculate a fixed overhead rate using budgeted costs, and factory capacity as the denominator-level concept (expressed in terms of output units).

$40,000 ÷ 20,000 boxes = $2.00 per box.

The advantage of using capacity in the denominator is that this denominator-level concept shows how low the fixed cost per unit can go, and hence, how low the total cost per unit can go, as production increases.

The fixed overhead spending variance is calculated as follows:

$42,000 actual - $40,000 budgeted = $2,000 unfavorable.

Next: we calculate the volume variance using capacity as the denominator-level concept:

volume variance = ($2.00 per box x 12,000 boxes) - $40,000 = $16,000 unfavorable

or equivalently:

volume variance = $2.00 per box x (12,000 boxes - 20,000 boxes) = $16,000 unfavorable

If the company uses a standard costing system, the amount of overallocated or underallocated fixed overhead is the difference between actual fixed overhead incurred, and fixed overhead allocated to product, calculated as follows:

actual fixed overhead - fixed overhead allocated

= $42,000 - ($2.00 per box x 12,000 boxes)

= $42,000 - $24,000 = $18,000 underallocated

This $18,000 of underallocated fixed overhead is equal to the sum of the $2,000 unfavorable fixed overhead spending variance and the $16,000 unfavorable volume variance.

Next: we calculate the volume variance using budgeted production as the denominator-level concept:

volume variance = ($4.00 per box x 12,000 boxes) - $40,000 = $8,000 favorable

or equivalently:

volume variance = $4.00 per box x (12,000 boxes - 10,000 boxes) = $8,000 favorable

actual fixed overhead - fixed overhead allocated

= $42,000 - ($4.00 per box x 12,000 boxes)

= $42,000 - $48,000 = $6,000 overallocated

This $6,000 of overallocated fixed overhead is equal to the sum of the $2,000 unfavorable fixed overhead spending variance (which did not change when we changed the denominator-level concept from capacity to budgeted production) and the $8,000 favorable volume variance.

To illustrate that the choice of allocation base does not affect the calculation of the volume variance, we recalculate the volume variance assuming the company allocates overhead using machine hours as the allocation base and budgeted production as the denominator-level concept. The budgeted overhead rate is now

$40,000 ÷ 500 machine hours = $80 per machine hour.

Since the standard for machine time is one hour for every twenty boxes (derived from the budget column in the box at the beginning of the example), the standard costing system will allocate fixed overhead as follows:

Budgeted overhead rate x (standard inputs allowed for actual outputs achieved)

= $80 per machine hour x (12,000 boxes ÷ 20 boxes per machine hour)

= $80 per machine hour x 600 machine hours = $48,000

And the volume variance is

fixed overhead allocated to product - budgeted fixed overhead

= $48,000 - $40,000 = $8,000 favorable, as before.

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For a printer-friendly version, contact Dennis Caplan at dcaplan@uamail.albany.edu