Materials  Recalculating standard Quantity/Cost for actual Output
Standards for Actual Output
The following standard and actual data relating to an output of 150 units would help us in identifying the variances.
Standard  Actual  

for SO  
SQ  SP  SC  AQ  AP  AC  
Material Used  450  4  1,800  440  5  2,200 
Output  150 SO  150 AO 
Output (_O) is in units, Quantities (_Q) are in kgs, Prices (_P) are in monetary value per unit quantity and Costs (_C) are in monetary values.
 Quantity of materials.
440 kgs actual as against a standard of 450 kgs indicating efficiency in using materials.
 Price of materials.
5 actual as against a standard price of 4 indicating inefficiency in purchasing materials.
 Cost of materials.
2,200 actual as against a standard cost of 1,800 indicating burden on account of cost of materials.
Why Recalculate Standards?
Standards may be expressed for any level of activity. Where standards are available for an output other than that has been actually achieved i.e. when Standard Output and Actual Output are not equal (SO ≠ AO), we cannot get an idea of the variance by comparing the available data.From the following data, we cannot straightaway say whether the output was obtained at a lesser or greater cost as well as whether the materials have been used efficiently.
Standard  Actual  

for SO  
SQ  SP  SC  AQ  AP  AC  
Material Used  2,250  2  4,500  480  2  960 
Output  1,000 SO  210 AO 
This is because the actual data pertains to an output of 210 units as against the standard known for an output of 1,000 units.
Comparing the quantities and costs for the actual output of 210 units with those of the standard output of 1,000 units is inappropriate. We cannot say that 480 kgs were actually used as against a standard of 2,250 kgs or the actual cost is 960 as against a standard cost of 4,500.
However we would be able to say that the materials were acquired at a price of 2 as indicated by the standard. This conclusion can be drawn in spite of the standard output and actual output being different.
To be able to make a meaningful comparison straight away, we have to recalculate the standards such that the outputs are the same both in the actual data and the standard data, thereby enabling us to derive variances by comparison.
The comparison becomes meaningful once we obtain the standards for the actual output
Standard  Actual  

for SO  for AO  
SQ  SP  SC  SQ(AO)  SC(AO)  AQ  AP  AC  
Material Used  2,250  2  4,500  472.5  945  480  2  960 
Output  1,000 SO  210 SO(AO)  210 AO 
 Quantity of materials.
480 kgs actual as against a standard of 472.5 kgs indicating inefficiency in using materials.
 Price of materials.
2 actual as against a standard price of 2 indicating efficiency in purchasing materials.
Note that we can draw this conclusion even without recalculating the standards.
 Cost of materials.
960 actual as against a standard cost 945 indicating a slight burden on account of cost of materials.
To find the variance in quantity of material used we need the standard quantity for actual output [SQ(AO)] and the variance in the cost of materials we need the standard cost for actual output [SC(AO)].
Since standards can be built for any production level we were able to recalculate the standards for the actual output.
Illustration  Problem (for explanation)
working table
The data from the problem obtained as it is, arranged in a working table.
Standard  Actual  

for SO  
SQ  SP  SC  AQ  AP  
Material A Material B Material C  900 800 200  15 45 85  2,250 1,950 550  16 42 90  
Total/Mix  1,900  66,500  4,750  
Output  1,800 SO  4,320 AO 
Output (_O) is in units of measurement of output, Quantities (_Q) are in units of measurement of input, Prices (_P) are in monetary value per unit input and Costs (_C) are in monetary values.
Assuming the input and output are in kgs for the purpose of explanations.
The Standard cost and loss data worked out and arranged in the working table.
Standard  Actual  

for SO  
SQ  SP  SC  AQ  AP  
Material A Material B Material C  900 800 200  15 45 85  13,500 36,000 17,000  2,250 1,950 550  16 42 90 
Total/Mix  1,900  35  66,500  4,750  
Input Loss  100  35  3,500  430  
Output  1,800 SO  4,320 AO 
SQIL = SI − SO
AQIL = AI − AO
SC = SQ × SP
Notice that SO ≠ AO.
We ignored other possible calculations like AC = AQ × AP, since we are only trying to recalculate standards primarily quantities and costs.
Factor  (AO)
Logic (based on Cost of Material_{A})
If SO is  SC is  
1,800 kgs  ⇒  13,500 
4,320 kgs  ⇒  ? 
Standard Cost for an Output of 4,320 kgs
=  13,500 ×
 
=  Standard Cost ×

AO 
SO 
AO 
SO 
Using the data in the illustration above,
(AO)  = 
 
= 
 
=  2.4 
Standard Quantity for Actual Output
AO 
SO 
For each Material separately
Standard Quantity of a Material for the Actual Output
SQ(AO)_{Mat} = SQ_{Mat} ×AO SO For all Materials together
Standard Quantity of Mix for Actual Output
SQ(AO)_{Mix} = SQ_{Mix} × AO SO Or = ΣSQ(AO)_{Mat} Sum of the Standard Quantity for Actual Output of Individual Materials
Using the data in the illustration above,
SQ(AO)_{A}  =  SQ_{A} ×
 
=  900 kgs × 2.4  =  2,160 kgs  
SQ(AO)_{B}  =  SQ_{B} ×
 
=  800 kgs × 2.4  =  1,920 kgs  
SQ(AO)_{C}  =  SQ_{C} ×
 
=  200 kgs × 2.4  =  480 kgs  
SQ(AO)_{Mix}  =  4,560 kgs  
SQ(AO)_{Mix}  =  SQ_{Mix} ×
 
=  1,900 kgs × 2.4  =  4,560 kgs 
Standard Cost for Actual Output
SC(AO)  =  SC ×
 
Or  =  SQ × SP ×
 
=  SQ ×
 
=  SQ(AO) × SP Standard Quantity for Actual Output × Standard Price 
For each Material separately
Standard Cost of a Material for Actual Output
SC(AO)_{Mat} = SC_{Mat} × AO SO Or = SQ(AO)_{Mat} × SP_{Mat} For all Materials together
Standard Cost of Mix for Actual Output
SC(AO)_{Mix} = SC_{Mix} × AO SO Or = SQ(AO)_{Mix} × SP_{Mix} Standard Price of Mix
SP_{Mix} = SC_{Mix} SQ_{Mix} = ΣSC_{Mat} ΣSQ_{Mat}
Using the data in the illustration above,
SC(AO)_{A}  =  SC_{A} ×
 
=  13,500 × 2.4  =  32,400  
SC(AO)_{B}  =  SC_{B} ×
 
=  36,000 × 2.4  =  86,400  
SC(AO)_{C}  =  SC_{C} ×
 
=  17,000 × 2.4  =  40,800  
SC(AO)_{Mix}  =  1,59,600  
SC(AO)_{Mix}  =  SC_{Mix} ×
 
=  66,500 × 2.4  =  1,59,600 
Alternative
If SQ(AO) and SP are readily available,
SC(AO)_{A}  =  SQ(AO)_{A} × SP_{A}  
=  2,160 kgs × 15/kg  =  32,400  
SC(AO)_{B}  =  SQ(AO)_{B} × SP_{B}  
=  1,920 kgs × 45/kg  =  86,400  
SC(AO)_{C}  =  SQ(AO)_{C} × SP_{C}  
=  480 kgs × 85/kg  =  40,800  
SC(AO)_{Mix}  =  1,59,600  
SC(AO)_{Mix}  =  SQ(AO)_{Mix} × SP_{Mix}  
=  4,560 kgs × 35/kg  =  1,59,600 
SP_{Mix}  = 
 
= 
 
=  35/kg 
Standard Quantity of Input Loss for Actual Output
Standard quantity of input loss for the actual output represents the input quantity that would have been lost for the actual output had the materials been used (quantity) as per the standard.
AO 
SO 
For each Material separately
Standard Quantity of input loss for the Actual Output
SQIL(AO)_{Mat} = SQIL_{Mat} ×AO SO Theoretically this measure can be calculated for each material separately. This would be of relevance only in cases where the input loss is being measured for each material separately and not over the mix.
For all Materials together
Standard Quantity of input loss of Mix for Actual Output
SQIL(AO)_{Mix} = SQIL_{Mix} × AO SO Or = ΣSQIL(AO)_{Mat} Sum of the Standard Quantity of input loss for Actual Output of Individual Materials
This would be relevant only when the input loss is being measured for each material separately.
Using the data in the illustration above,
SQIL(AO)_{A}  =  SQIL_{A} ×
 
=  NA  =  NA  
SQIL(AO)_{B}  =  SQIL_{B} ×
 
=  NA  =  NA  
SQIL(AO)_{C}  =  SQIL_{C} ×
 
=  NA  =  NA  
SQIL(AO)_{Mix}  =  NA  
SQIL(AO)_{Mix}  =  SQIL_{Mix} ×
 
=  100 kgs × 2.4  =  240 kgs 
Standard Cost of Input Loss for Actual Output
SCIL(AO)  =  SCIL ×
 
Or  =  SQIL × SP ×
 
=  SQIL ×
 
=  SQIL (AO) × SP Standard Quantity of Input Loss × Standard Price 
For each Material separately
Standard Cost of Input Loss of a Material for Actual Output
SCIL(AO)_{Mat} = SC_{Mat} × AO SO Or = SQIL (AO)_{Mat} × SP_{Mat} For all Materials together
Standard Cost of Input Loss of Mix for Actual Output
SCIL(AO)_{Mix} = SC_{Mix} × AO SO Or = SQIL (AO)_{Mix} × SP_{Mix} Standard Price of Mix
SP_{Mix} = SI SQ = ΣSC_{Mat} ΣSQ_{Mat}
Using the data in the illustration above,
SCIL(AO)_{A}  =  SC_{A} ×
 
=  NA  =  NA  
SCIL(AO)_{B}  =  SC_{B} ×
 
=  NA  =  NA  
SCIL(AO)_{C}  =  SC_{C} ×
 
=  NA  =  NA  
SCIL(AO)_{Mix}  =  NA  
SCIL(AO)_{Mix}  =  SC_{Mix} ×
 
=  3,500 × 2.4  =  8,400 
Alternative
If SQIL (AO) and SP are readily available,
SCIL(AO)_{A}  =  SQIL (AO)_{A} × SP_{A}  
=  NA  =  NA  
SCIL(AO)_{B}  =  SQIL (AO)_{B} × SP_{B}  
=  NA  =  NA  
SCIL(AO)_{C}  =  SQIL (AO)_{C} × SP_{C}  
=  NA  =  NA  
SCIL(AO)_{Mix}  =  NA  
SCIL(AO)_{Mix}  =  SQIL (AO)_{Mix} × SP_{Mix}  
=  240 kgs × 35/kg  =  8,400 
SP_{Mix}  = 
 
= 
 
=  35/kg 
Data Table with the recalculated Standard
The data for the standards based on the actual output is as below.
Standard  Actual  

for SO  for AO  
SQ  SP  SQ(AO)  SC(AO)  AQ  AP  
Factor  2.4  
Material A Material B Material C  900 800 200  15 45 85  2,160 1,920 480  32,400 86,400 40,800  2,250 1,950 550  16 42 90 
Total/Mix  1,900  4,560  1,59,600  4,750  
Input Loss  100  240  8,400  430  
Output  1,800 SO  4,320 SO(AO)  4,320 AO 
1.  (AO)  = 
 
= 
 
=  2.4 
Using this factor, (AO), the SQ(AO) and SQIL(AO), from that the SC(AO) and SCIL(AO) can be calculated straight away in the working table. To make these calculations convenient and avoid errors, present this factor also in the working table.
2.  SQ(AO)  =  SQ ×
 
=  SQ × 2.4 
3. SC(AO) = SQ(AO) × SP
4.  SP_{Mix}  = 

SP_{Mix} will be required to calculate SC_{Mix} and SCIL_{Mix} directly using a formula, instead of as the sum of the values for the constitutent materials.
5. SO(AO) = AO
6.  SQIL(AO)  =  SQIL ×
 
=  SQIL × 2.4 
7. SCIL(AO) = SQIL(AO) × SP
After recalculating the standards we have Actuals and S_(AO) whose output values are the same.