The twoway analysis of factory overhead shows the difference between the total actual and total standard FOH costs split into two components: budget variance and volume variance.
It takes into consideration the total cost of FOH, both fixed and variable.
Components of the TwoWay Analysis
The twoway analysis consists of: 1.) budget variance (also known as controllable variance), and 2.) volume variance.
These variances represent a combination of the different variances we've discussed in other lessons.
Budget variance  =  Variable spending variance + Variable efficiency variance + Fixed budget variance 
Volume variance  =  Fixed volume variance 
Alternatively, the budget variance may be computed as the difference between actual factory overhead and budget allowed based on standard hours. If the actual FOH is greater than the budget allowed, the variance is unfavorable; otherwise, favorable.
The volume variance is the difference between the budget allowed on standard hours and the standard factory overhead. If the budget allowed is greater than the standard FOH, the variance is unfavorable.
Example
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  
Total  $130,750 
The twoway analysis variances can be computed as follows:
BUDGET VARIANCE  
Actual FOH  $130,750 

Budget allowed on standard hours  129,000 

*for variable (1,100 x 3 hours x $30)  
*for fixed ($30,000 as budgeted)  
Budget variance  $ 1,750 
UF 

VOLUME VARIANCE  
Budget allowed on standard hours  $129,000 

Standard FOH (1,100 x 3 hours x $40)  132,000 

Volume variance  $ 3,000 
F 

TOTAL FACTORY OVERHEAD VARIANCE  $ 1,250 
F 
The favorable variance of $1,250 in total factory overhead costs is brought about by a $1,750 unfavorable budget variance and a $3,000 favorable volume variance.