Variable Overheads » Cost Variance = Expenditure Variance + Efficiency Variance



The Variable Overhead Cost variance which is the difference between the variable overhead absorbed and variable overhead incurred is sub divided into two as variable overhead expenditure variance and variable overhead efficiency variance.
• Mathematical Derivation of the Constituents
Knowing how the cost variance is segregated into expenditure and efficiency may aid your understand and recollection of the formulae.
Where
 VOHCA = Variable Overhead Cost Absorbed
 VOHCI = Variable Overhead Cost Incurred
 VOHCV = Variable Overhead Cost Variance
 VOHExpV = Variable Overhead Expenditure Variance
 VOHEffV = Variable Overhead Efficiency Variance
 SVOHC = Standard Variable Overhead Cost
Variable Overhead Cost Variance 
= 
Variable Overhead Absorbed − Variable Overhead Incurred 
VOHCV 
= 
VOHCA − VOHCI 

= 
VOHCA − VOHCI + SVOHC − SVOHC
[Adding and deducting SVOHC]


= 
(VOHCA − SVOHC) + (SVOHC − VOHCI) 

= 
VOHEffV + VOHExpV 
• Efficiency Variance
Thus,
Variable Overhead Efficiency Variance 
= 
Variable Overhead Cost Absorbed − Standard Variable Overhead Cost 
⇒ VOHEffV 
= 
VOHCA − SVOHC 
Efficiency variance is the difference between the variable overheads that should have been incurred as per standards and the overheads that have been absorbed into cost.
• Expenditure Variance
Thus,
Variable Overhead Expenditure Variance 
= 
Standard Variable Overhead Cost − Variable Overhead Cost Incurred 
⇒ VOHExpV 
= 
SVOHC − VOHCI 
Expenditure variance is the difference between the variable overheads that should have been incurred as per standards and the actual expenditure incurred.

The Formulae » Variable Overhead Expenditure Variance (VOHExV)



The Variable Overhead Expenditure Variance gives an idea of how much more or less the actual variable overhead cost incurred is when compared to the standards.
⇒ Variable Overhead Expenditure Variance = Standard Variable Overhead Cost − Variable Overhead Cost Incurred
⇒ VOHExpV = SVOHC  VOHCI
Variable Overhead Cost Incurred

= 
(Actual Output × Actual Rate/unit) 
⇒ VOHCI

= 
(AO × AR/U) 
(Or) 
= 
(Actual Time × Actual Rate/hour) 
(Or) 
= 
(AT × AR/H) 
• Note
 Time is measured in hours in most cases. It may be in other units also.
 Actual Rate/unit ⇒ Actual Variable Overhead Absorption Rate per unit
 Actual Rate/hour ⇒ Actual Variable Overhead Absorption Rate per hour
• Overheads Absorbed on Unit Rate Basis
» Calculations based on Output (in Units)
Standard Variable Overhead Cost

= 
(Standard Output for Actual Time × Budgeted Rate/Unit) 
⇒ SVOHC

= 
SO for AT × BR/U 
(Or)

= 

Therefore, 
VOExpV

= 
SVOHC − VOHCI 


= 
({AT × 

} × BR/U) − (AO × AR/U) 

♣ Budgeted Rate/unit ⇒ Budgeted Variable Overhead Absorption Rate per unit
» Calculations based on Input (Time in Hours)
Standard Variable Overhead Cost

= 
Actual Time × Budgeted Rate/hour 
⇒ SVOHC

= 
AT × BR/H 
Therefore, 
VOHExpV

= 
SVOHC − VOHCI 


= 
(AT × BR/H) − (AT × AR/H) 
♣ Budgeted Rate/hour ⇒ Budgeted Variable Overhead Absorption Rate per hour
• Overheads Absorbed on Time (Hours) Basis
» Calculations based on Input (Time in Hours)
Standard Variable Overhead Cost

= 
(Standard Time for Actual Output × Budgeted Rate/hour) 
⇒ SVOHC

= 
ST for AO × BR/H 
(Or)

= 

Therefore, 
VOExpV

= 
SVOHC − VOHCI 


= 
({AO × 

} × BR/H) − (AT × AR/H) 

♣ Budgeted Rate/hour ⇒ Budgeted Variable Overhead Absorption Rate per hour
» Calculations based on Output (in Units)
Standard Variable Overhead Cost

= 
Actual Output × Budgeted Rate/unit 
⇒ SVOHC

= 
AO × BR/U 
Therefore, 
VOHExpV

= 
SVOHC − VOHCI 


= 
(AO × BR/U) − (AO × AR/U) 
♣ Budgeted Rate/unit ⇒ Budgeted Variable Overhead Absorption Rate per unit
The choice of the formula that we use is dependent on two factors
 The actual basis for absorption used and
 The basis we chooce for calculations.
Care should be taken to ensure that we do not simply interchange the actual units and actual time in calculating absorbed overheads.


Variable Overhead Expenditure Variance » Formula Interpretation



The variance would be Nil where the Standard overhead cost and the incurred overhead cost are the same.
In problem solving it would be convenient interpreting these formulae in terms of value identifiers rather than the factors that are used to derive value. Thus you need to find the absorbed overhead and there are various formulae for finding the absorbed overhead. This is what you need to remember.

A factory was to budgeted to produce 2,000 units of output @ one unit per 10 hours productive time working for 25 days. Rs. 40,000 of variable overhead cost and Rs. 80,000 of fixed overhead cost were budgeted to be incurred during that period.
The factory worked for 26 days putting in 860 hours work every day and achieved an output of 2,050 units. The expenditure incurred as overheads was Rs. 49,200 as variable overheads and Rs. 86,100 as fixed overheads.
What is the variation in total overhead cost on account of a variation in the variable overhead expenditure?
This information is provided by the variable overhead expenditure variance

The problem data arranged in a working table:
Particulars 
Budgeted 
Actual 
a) Output

2,000 
2,050 
b) Working Days

25 
26 
c) Total Time Worked (in hrs)

20,000 
22,360 
d) Overhead Cost (in Rs.)
Variable
Fixed
Total

40,000 80,000 1,20,000

49,200 86,100 1,35,300

e) Overhead Rates [(d) ÷ (a)] (in Rs./Unit)
Variable [(40,000 ÷ 2,000)]
Fixed [(80,000 ÷ 2,000)]
Total [(1,20,000 ÷ 2,000)]

20 40 60


f) Overhead Rates [(d) ÷ (c)] (in Rs./hr)
Variable [(40,000 ÷ 20,000)]
Fixed [(80,000 ÷ 20,000)]
Total [(1,20,000 ÷ 20,000)]

2 4 6


• Note
This working table gives all the data that would be needed to solve a problem involving all overhead variances. In Calculating only the total overhead cost variance you may not need all that data.
We give it here so that you get accustomed to preparing the working table by the time you complete going through all the overhead variances.

• Working Time
» Budgeted Time [BT]
BT 
= 
Budgeted Output × Budgeted Time/unit 

= 
2,000 units × 10 labor/labour hrs/unit
[@ one unit per 10 hours productive time]


= 
20,000 labor/labour hrs 
» Actual Time [AT]
AT 
= 
Number of Days × Actual Time/day 

= 
26 days × 860 labour/labor hrs/day 

= 
22,360 labor/labour hrs 

Solution [Overheads Absorbed on Unit basis]



» Calculations Based on Output (in Units)
Standard Variable Overhead Cost

= 
(Standard Output for Actual Time × Budgeted Rate/Unit) 
⇒ SVOHC

= 


= 
{22,360 hrs × 

} × Rs. 20/unit 


= 
Rs. 22,360 × 0.1 × 20 

= 
Rs. 44,720 
» Calculations Based Input (Time in Hours)
Standard Variable Overhead Cost

= 
(Actaul Time × Budgeted Rate/Hour) 
⇒ SVOHC

= 
AT × BR/H 

= 
22,360 hrs × Rs. 2/hour 

= 
Rs. 44,720 
• Calculation of Expenditure Variance
VOHExpV 
= 
Standard Variable Overhead Cost − Variable Overhead Cost Incurred 

= 
Rs. 44,720 − Rs. 49,200 

= 
− Rs. 4,480 [Adv] 
The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

Solution [Overheads Absorbed on Time basis]



» Calculations Based on Input (Time in hours)
Standard Variable Overhead Cost

= 
(Standard Time for Actual Output × Budgeted Rate/Hour) 
⇒ SVOHC

= 


= 
{2,050 units × 

} × Rs. 2/hour 


= 
Rs. 2,050 × 10 × 2 

= 
Rs. 41,000 
• Calculations Based on Output (in Units)
Standard Variable Overhead Cost

= 
(Actaul Output × Budgeted Rate/Unit) 
⇒ SVOHC

= 
AO × BR/U 

= 
2,050 units × Rs. 20/unit 

= 
Rs. 41,000 
• Calculation of Expenditure Variance
VOHExpV 
= 
Standard Variable Overhead Cost − Variable Overhead Cost Incurred 

= 
Rs. 41,000 − Rs. 49,200 

= 
− Rs. 8,280 [Adv] 
The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

With regard to the basis adopted for absorption of overhead we do not have a choice. It is something decided upon by the organisation.
Where the absorption has been made on unit basis, we can arrive at the absorbed overhead using the data relating to time (if it is available). Similarly, where absorption has been made on time basis, can arrive at the absorbed overhead using the data relating to output (if it is available).
Where data relating to both time and output are available, the first thing that we need to decide upon is the basis for absorption adopted. Where nothing is mentioned, we generally assume that unit basis has been adopted for absorption of overhead. In the absence of data relating to output we may assume that the absorption has been made on time basis also.
Thus availability of data is one another factor that would decide which formula we have to use. However, even in such a case, we need to decide upon the basis for absorption that has been adopted and then use a relevant formula based on the data available.
Be aware that you should not simply replace AT with AO and BR/hr with BR/U, as
Absorbed Overhead is equal to
 AT × BR/hr (Or = SO for AT × BR/hr) ← Absorption based on Time
 AO × BR/U (Or = BT for AO × BR/U) ← Absorption based on Units

Formulae using Interrelationships among Variances



 VOHCV = VOHExpV + VOHEffV → (1)
From (1)
VOHExpV = VOHCV − VOHEffV

• Verification
The interrelationships between variances would also be useful in verifying whether our calculations are correct or not. After calculating the two variable overhead variances we can verify whether VOHExpV and VOHEffV add up to VOHCV or not. If VOHExpV + VOHEffV = VOHCV we can assume our calculations to be correct.


