Three-Way Factory Overhead Variance Analysis

The three-way analysis shows the difference between the total actual factory overhead and total standard factory overhead costs split into three components: spending variance, efficiency variance, and volume variance.

Components of the Three-Way Analysis

The three-way analysis consists of: 1.) spending variance, 2.) efficiency variance, and 3.) volume variance. The spending variance consists of the variable spending variance and fixed spending variance (a.k.a. fixed budget variance).

Spending variance = Variable spending variance + Fixed budget variance
Efficiency variance = Variable efficiency variance
Volume variance = Fixed volume variance

Alternatively, the spending variance may be computed as the difference between actual factory overhead and budget allowed based on actual hours (BAAH). If the actual FOH is greater than the BAAH, the variance is unfavorable; otherwise, favorable.

The efficiency variance is the difference between the BAAH and the budget allowed based on standard hours (BASH). If the BAAH is greater than the BASH, the variance is unfavorable.

And finally, the volume variance is the difference between the BASH and the standard factory overhead. Also, if the BAAH is greater than the standard FOH, the variance is unfavorable.


Company XYZ produces a product that has the following factory overhead standard costs per unit. The budgeted production is at the normal capacity of 1,000 units, requiring a budgeted time of 3,000 hours. The total fixed factory overhead at this capacity is $30,000.

Variable FOH 3 hours at $30 per hour
Fixed FOH 3 hours at $10 per hour

During the month, the company produced 1,100 units and incurred the following actual factory overhead costs:

Variable FOH 3,250 hours at $29 per hour $  94,250
Fixed FOH   $  36,500

The three-way analysis variances can be computed as follows:

  Actual FOH (variable + fixed)
  Budget allowed on actual hours (BAAH)
     *for variable (3,250 hours x $30)    
     *for fixed ($30,000 as budgeted)    
  Budget variance
$   3,250
  Budget allowed on actual hours (BAAH)
  Budget allowed on standard hours (BASH)
     *for variable (1,100 x 3hours x $30)    
     *for fixed ($30,000 as budgeted)    
  Efficiency variance
$   1,500
  Budget allowed on standard hours (BASH)
  Standard FOH (1,100 x 3 hours x $40)
  Volume variance
$   3,000
$   1,250

Four-Way Analysis

A more expanded breakdown known as "four-way analysis" simply separates the spending variance into the variable and fixed components. The four-way analysis consists of: 1.) variable spending variance, 2.) fixed spending variance, 3.) efficiency variance, and 4.) volume variance.

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