The Formulae » Total Overhead Cost Variance (TOHCV)

# ⇒ Total Overhead Cost Variance = Total Overhead Cost Absorbed − Total Overhead Cost Incurred ⇒ TOHCV = TOCA - TOCI

 ⇒ TOHCI (AO × AR/U) (AT × AR/H) Total Overhead Cost Incurred = (Actual Output × Actual Rate/unit) = (Or) = (Actual Time × Actual Rate/hour) (Or) =

## • Note

1. Time is measured in hours in most cases. It may be in other units also.
2. Actual Rate/unit ⇒ Actual Total Overhead Absorption Rate per unit
3. Actual Rate/hour ⇒ Actual Total Overhead Absorption Rate per hour

# • Overheads Absorbed on Unit Rate Basis

## » Calculations based on Output (in Units)

 ⇒ TOHCA AO × BR/U Total Overhead Cost Absorbed = (Actual Output × Budgeted Rate/unit) =

 TOCV (AO × BR/U) − (AO × AR/U) Therefore, = TOHCA − TOHCI =

♣ Budgeted Rate/unit ⇒ Budgeted Total Overhead Absorption Rate per unit

## » Calculations based on Input (Time in Hours)

Total Overhead Cost Absorbed = (Standard Time for Actual Output × Budgeted Rate/hour)
⇒ TOHCA = ST for AO × BR/H
(Or) =
{AO ×
 BT BO
} × BR/H

Therefore, TOCV = TOHCA − TOHCI
=
({AO ×
 BT BO
} × BR/H) − (AT × AR/H)

♣ Budgeted Rate/hour ⇒ Budgeted Total Overhead Absorption Rate per hour

# • Overheads Absorbed on Time (Hours) Basis

## » Calculations based on Input (Time in Hours)

 ⇒ TOHCA (AT × BR/H) Total Overhead Cost Absorbed = (Actual Time × Budgeted Rate/hour) =

 TOCV (AT × BR/H) − (AT × AR/H) Therefore, = TOHCA − TOHCI =

♣ Budgeted Rate/hour ⇒ Budgeted Total Overhead Absorption Rate per hour

## » Calculations based on Output (in Units)

Total Overhead Cost Absorbed = (Standard Output for Actual Time × Budgeted Rate/Unit)
⇒ TOHCA = SO for AT × BR/U
(Or) =
{AT ×
 BO BT
} × BR/U

Therefore, TOCV = TOHCA − TOHCI
=
({AT ×
 BO BT
} × BR/U) − (AO × AR/U)

♣ Budgeted Rate/unit ⇒ Budgeted Total 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 choose for calculations. Care should be taken to ensure that we do not simply interchange the actual units and actual time in calculating absorbed overheads.

 Total Overhead Cost Variance » Formula Interpretation
 The variance would be Nil where the absorbed overhead and the incurred overhead 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 Problem
 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? This information is provided by Total Overhead Cost Variance

 Solution » Working Table
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
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.

 Solution » Working Notes

# » 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)

 ⇒ TOHCA AO × BR/U Total Overhead Cost Absorbed = (Actual Output × Budgeted Rate/unit) = = 2,050 units × Rs. 60/unit = Rs. 1,23,000

## » Calculations Based on Time

Total Overhead Cost Absorbed = (Standard Time for Actual Output × Budgeted Rate/hour)
⇒ TOHCA =
{AO ×
 BT BO
} × BR/H
=
{2,050 units ×
 20,000 hrs 2,000 units
} × Rs. 6/hr
= 2,050 units × 10 hrs/unit × Rs. 6/hr
= Rs. 1,23,000

# • Calculation of Cost Variance

= Rs. 1,23,000 − Rs. 1,35,300

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)

 ⇒ TOHCA (AT × BR/H) Total Overhead Cost Absorbed = (Actual Time × Budgeted Rate/hour) = = 22,360 hrs × Rs. 6/hr = Rs. 1,34,160

## » Calculations Based on Units

Total Overhead Cost Absorbed = (Standard Output for Actual Time × Budgeted Rate/Unit)
⇒ TOHCA =
{AT ×
 BO BT
} × BR/U
=
{22,360 hrs ×
 2,000 units 20,000 hrs
} × Rs. 60/unit
= 22,360 hrs × 0.1 units/hr × Rs. 60/unit
= Rs. 1,34,260

# • Calculation of Cost Variance

= Rs. 1,34,160 − Rs. 1,35,300

The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

 Which method to choose?

 Formulae using Inter-relationships among Variances
1. TOHCV = VOHCV + FOHCV   → (1)

From (1)
 TOHCV = VOHCV + FOHCV

2. VOHCV = VOHExpV + VOHEffV   → (2)

From (1) and (2)
 TOHCV = VOHExpV + VOHEffV + FOHCV

3. FOHCV = FOHVolV + FOHExpV   → (3)

From (1), (2) and (3)
 TOHCV = VOHExpV + VOHEffV + FOHVolV + FOHExpV

4. FOHVolV = FOHCalV + FOHCapV + FOHEffV   → (4)

From (1), (2), (3) and (4)
 TOHCV = VOHExpV + VOHEffV + FOHCalV + FOHCapV + FOHEffV + FOHExpV

## • Verification

The interrelationships between variances would also be useful in verifying whether our calculations are correct or not. After calculating the three variances we can verify whether FOHCV and VOHCV add up to TOHCV or not. If FOHCV + VOHCV = TOHCV we can assume our calculations to be correct.
 Author Credit : The Edifier ... Continued Page O:7