Based on their nature, Losses are classified into two:
Normal Loss
Those losses whose occurrence is inevitable i.e. which occur on account of normal reasons. Normal Loss is valued at its market price or the net realisable value.
Abnormal Loss
Those losses whose occurrence can be avoided i.e. which occur on account of abnormal reasons. Abnormal Loss is valued at cost or its full value.

Ascertaining Output using Loss Data



The data relating to output can be ascertained as:
 Actual Output = Actual Quantity of Actual Mix − Actual Loss
 Standard Output = Standard Quantity of Standard Mix − Standard Loss
Loss of Mix
In dealing with losses in calculating material variances we deal with only loss of mix and not loss of individual materials.

Influence of Losses in calculation of Variances



We use the data relating to the quantity of losses only to ascertain the Standard Output (SO) and Actual Output (AO) if they are not given. If they i.e. SO and AO are known, we can just ignore the data relating to the quantity of losses.
The value of loss whether normal or abnormal is not considered in calculating material variances. This is done by considering the SC_{Mix} at its Gross value in calculating the SP(SO).
When the standard data includes details relating to the loss it is obvious that it is a "Normal Loss", i.e. the acceptable loss in the production process. The standard price given for the loss indicates the market price for the normal loss (Since, "Normal Loss is valued at Market Price or Net Realisable Value").
The problems involving losses can be classified into two types
Input and Output in same terms
Problems where Input and Output are in the same terms.
[Eg: Input is given in kilograms and the output is also in kilograms.]
Consider the following data arranged in a working table:

Standard [Production: ???] 
Actual [Production: ???] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material X 
500 
10 
5,000 
470 
11 
5,170 
Material Y 
700 
25 
17,500 
700 
24 
16,800 
Total
 1,200 

22,500 
1,170 

21,970 
Less: Loss @10%
 120 
10 
1,200 
110 


Standard Output and the Actual Output are not given. Assuming that the Output would be in the same terms as the input i.e. in kgs,
The data relating to output can be ascertained as:
 Using, AO = AQ_{Mix} − AL_{Mix}
• AO 
= 
1,170 kgs − 110 kgs 

= 
1,060 kgs 
 Using, SO = SQ_{Mix} − SL_{Mix}
• SO 
= 
1,200 kgs − 120 kg 

= 
1,080 kg 
Where the data relating to the Standard Output and Actual Output are given, these calculations are not necessary.

Standard [Production: 1,080 kg] 
Actual [Production: 1,060 kg] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material X 
500 
10 
5,000 
470 
11 
5,170 
Material Y 
700 
25 
17,500 
700 
24 
16,800 
Total/Gross
 1,200 

22,500 
1,170 

21,970 
Less: Loss @10%
 120 
10 
1,200 
110 


Net
 1,080 

22,500 
1,060 

21,970 
Cost Data
The data relating to the realisable value of normal loss stock is to be ignored even if it is available (Rs. 1,200 for the standard). The Standard (Gross) Cost of the Mix is Rs. 22,500 and the Standard (Net) Cost of the Mix is Rs. 20,300 (Rs. 22,500 − Rs. 1,200).
You would be required to calculate the "Standard Price of Output" SP(SO), for which you need the "Standard Cost of Mix" SC_{Mix}. The gross cost should be taken as the cost and not the net cost. To ensure that you do not consider improper data, understand that you need to ignore the data relating to realisable value of normal loss.
Input and Output are in different Terms
Problems where Input and Output are in the different terms.
[Eg: Input is given in kilograms and the output is expressed in units.]

Standard [Production: 2000 units] 
Actual [Production: 1800 units] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material X 
500 
10 
5,000 
470 
11 
5,170 
Material Y 
700 
25 
17,500 
700 
24 
16,800 
Total
 1,200 

22,500 
1,170 

21,970 
Less: Loss @10%
 120 
10 
1,200 
110 


Net
 – 

22,500 
– 

– 
The data relating to losses is useful only for the purpose of ascertaining the standard or actual output as needed (if they are not given). If you are given the data relating to the final output (both Standard and Actual), you can ignore the data relating to losses.
If you are not given the data relating to outputs, you should be given some relationship between the losses and the outputs so that you would be able to identify the outputs using the data.
With regard to cost, you shoud consider the Standard (Gross) cost of the mix for calculating the SP(SO).
Why is value of loss ignored
Consider the standard data above.
In accounting or cost accounting, cost implies the normal cost (Rs. 21,300) which is the total cost (Rs. 22,500) reduced by the realisable value of normal loss (Rs. 1,200). Therefore, the cost incurred for the manufacture of 2,000 units of output should be Rs. 21,300 and not Rs. 22,500.
In such a case, in considering the actual data also the value of normal loss relating to the actual input should be eliminated to obtain the normal cost incurred.
However, while calculating the Quantity/Usage Variance we consider each material separately which would amount to considering the gross input and the gross cost for calculations. Thereby, when calculating the "Yield Variance" which is a part of the usage variance, we should also ensure that the gross input and the gross cost are taken into consideration by ignoring the data relating to losses.
If at all adjustments for normal losses have to be made, they are to be made both for the purpose of calculating the usage/quantity variance and yield variance. This would require us to distribute the normal loss both in terms of quantity as well as value over the three input materials which in itself would be a complicated process and not a perfect one. That is the reason the influence of losses and their realisations is ignored for the purpose of identifying material variances.

The Formulae » Material Yield Variance using Loss data



In terms of losses, the Material Yield Variance is the difference between the Standard Cost of Standard Loss for Actual Mix and the Standard Cost of Actual Loss
Material yield variance = Standard Cost of Standard Loss for Actual Quantity
− Standard Cost of Actual Loss
Note:
This formula can be used in all cases i.e. both when AQ _{Mix} = SQ _{Mix} as well as when AQ _{Mix} ≠ SQ _{Mix}. When AQ _{Mix} ≠ SQ _{Mix}, AQ _{Mix}/SQ _{Mix} works as an adjustment factor to readjust the Standard to Standard for Actual Input.
When AQ_{Mix} = SQ_{Mix}
When AQ_{Mix} = SQ_{Mix}, 

becomes 1 thus nullifying its effect, in which case the formula would read as:

In such a case, the formula would read
TMYV/TMSUV = (SL_{Mix} − AL_{Mix}) × SP(SO) 
Standard − Actual or Actual − Standard??
Say the actual loss is 200 kgs and the standard loss for actual input is 180 kgs.
Does this indicate efficiency or inefficiency?
Inefficiency for sure, since the loss was 200 kgs where it should have been 180 kgs.
This then should give us a negative variance, which would be possible only if we consider the data in the order "Standard" − "Actual".
Be conscious of this, as in calculating material yield variance using outputs we write, we write "Actual" − "Standard".

Solution [Using the data as it is]



For working out problems with the data considered as it has been given without having to do any recalculations, use the above formulae (which are capable of being used in all cases)
Consider the working table above:

Standard [Production: ??? (SO)] 
Actual [Production: ??? (AO)] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material X 
1,500 
10 
15,000 
2,400 
11 
26,400 
Material Y 
1.000 
25 
25,000 
1,500 
24 
36,000 
Total
 2,500 

40,000 
3,900 

62,400 
Less: Loss @10%
 250 
1 
250 



Actual
 


500 


Net
 2,250 


3,400 


Since the output data is not given, we calculate output from the given data.
Using,
SO 
= 
SQ_{Mix} − SL_{Mix} 
⇒ SO 
= 
2,500 kgs − 250 kgs 
⇒ SO 
= 
2,250 kgs 
Using,
AO 
= 
AQ_{Mix} − AL_{Mix} 
⇒ AO 
= 
3,900 kgs − 500 kgs 
⇒ AO 
= 
3,400 kgs 
Using
SP(SO) 
= 

⇒ SP(SO) 
= 

⇒ SP(SO) 
= 

Using,
TMYV/TMSUV 
= 
({ 

× SL_{Mix}} − AL_{Mix}) × SP(SO) 

• TMYV/TMSUV 
= 
({ 

× 250 kgs} − 500 kgs) × Rs. 

/kg 


= 
(390 kgs − 500 kgs) × Rs. 

/kg 


= 


= 
− Rs. 1,955.56 [Adv] 
Check:
MYV using the formula for output,
• TMYV/TMSUV 
= 
(3,400 − { 

× 2,250}) × Rs. 

/kg 


= 
(3,400 kgs − 3,510 kgs) × Rs. 

/kg 


= 


= 
− Rs. 1,955.56 [Adv] 

Solution [Using recalculated data]



Where you find that the SQ _{Mix} ≠ AQ _{Mix}, you may alternatively recalculate the standard to make the SQ _{Mix} = AQ _{Mix} and use the figures relating to the recalculated standard in the working table. In such a case, the formulae that you use would look simpler (without the adjustment factor AQ _{Mix}/SQ _{Mix}).
From the data relating to the problem, it is evident that SQ_{Mix} ≠ AQ_{Mix}. Thus we recalculate the standard data for Actual Input [Refer to the calculations].
Consider the recalculated standard data and the actual data arranged in a working table.

Standard [Production: ??? (SO)] 
Actual [Production: ??? (AO)] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material X 
2,340 
10 
23,400 
2,400 
11 
26,400 
Material Y 
1.560 
25 
39,000 
1,500 
24 
36,000 
Total
 3,900 

62,400 
3,900 

62,400 
Less: Loss @10%
 390 
1 
390 



Actual
 


500 


Net
 3,510 


3,400 


Since the output data is not given, we calculate output from the given data.
Using,
SO 
= 
SQ_{Mix} − SL_{Mix} 
⇒ SO 
= 
3,900 kgs − 390 kgs 
⇒ SO 
= 
3,510 kgs 
Using,
AO 
= 
AQ_{Mix} − AL_{Mix} 
⇒ AO 
= 
3,900 kgs − 500 kgs 
⇒ AO 
= 
3,400 kgs 
Using
SP(SO) 
= 

⇒ SP(SO) 
= 

⇒ SP(SO) 
= 

Using,
TMYV/TMSUV 
= 
(SL_{Mix} − AL_{Mix}) × SP(SO)

• TMYV/TMSUV 
= 
(390 kgs − 500 kgs) × Rs. 

/kg 


= 


= 
− Rs. 1,955.56 [Adv] 
Check:
MYV using the formula for output,
• TMYV/TMSUV 
= 
(3,400 − { 

× 2,250}) × Rs. 

/kg 


= 
(3,400 kgs − 3,510 kgs) × Rs. 

/kg 


= 


= 
− Rs. 1,955.56 [Adv] 
Note:
This formula can be used only when AQ _{Mix} = SQ _{Mix}.
You don't need to recalculate the standard
The formula with the adjustment factor AQ _{Mix}/SQ _{Mix} can be used in all cases i.e. both when AQ _{Mix} = SQ _{Mix} and AQ _{Mix} ≠ SQ _{Mix}. Therefore, you don't need to rebuild the working table by recalculating the standards for the purpose of finding the variances.
Check:
The same problem was solved in both the cases above. The only difference being that in the second case, the data was considered by recalculating the Standard for Actual Input to make AQ _{Mix} = SQ _{Mix}.

It is the difference between the Standard Cost of Standard Loss for Actual Output and the Standard Cost of Actual Loss
Material yield variance = Standard Cost of Standard Loss for Actual Ouptut − Standard Cost of Actual Loss
Note:
This formula can be used in all cases i.e. both when AO = SO as well as when AO ≠ SO. When AO ≠ SO, AO/SO works as an adjustment factor to readjust the Standard to Standard for Actual Output.
 The above formula can be used in all cases i.e. both when AO = SO or when AO ≠ SO. When AO = SO the factor AO/SO will become 1 thus nullifing its effect.
In such a case, both the formula would read
TMYV/TMSUV = (SL_{Mix} − AL_{Mix}) × SP_{Mix} 
Standard − Actual or Actual − Standard??
Say the actual loss is 200 kgs and the standard loss for actual input is 180 kgs.
Does this indicate efficiency or inefficiency?
Inefficiency for sure, since the loss was 200 kgs where it should have been 180 kgs.
This then should give us a negative variance which is possible only if we consider the data in the order "Standard" − "Actual".
Be conscious of this, as in calculating material yield variance using outputs we write, we write "Actual" − "Standard".

Solution [Using the data as it is]



For working out problems with the data considered as it has been given without having to do any recalculations, use the above formulae (which are capable of being used in all cases)
Consider the working table above:

Standard [Production: ??? (SO)] 
Actual [Production: ??? (AO)] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material X 
1,500 
10 
15,000 
2,400 
11 
26,400 
Material Y 
1.000 
25 
25,000 
1,500 
24 
36,000 
Total
 2,500 

40,000 
3,900 

62,400 
Less: Loss @10%
 250 
1 
250 



Actual
 


500 


Net
 2,250 


3,400 


Using,
SP_{Mix} 
= 

⇒ SP_{Mix} 
= 

⇒ SP_{Mix} 
= 
Rs. 16/kg 
Using,
TMYV/TMSUV 
= 
({ 

× SL_{Mix}} − AL_{Mix}) × SP_{Mix} 

• TMYV/TMSUV 
= 
({ 

× 250 kgs} − 500 kgs) × Rs. 16/kg 


= 
({ 

kgs} − 500 kgs) × Rs. 16/kg 


= 


= 


= 
− Rs. 1,955.56 [Adv or Unf] 

Solution [Using recalculated data]



Where you find that the SO ≠ AO, you may alternatively recalculate the standard to make the SO = AO and use the figures relating to the recalculated standard in the working table. In such a case, the formulae that you use would look simpler (without the adjustment factor AO/SO).
From the data relating to the problem, it is evident that SO ≠ AO. Thus we recalculate the standard data for Actual Input [Refer to the calculations].
Consider the recalculated standard data and the actual data arranged in a working table.

Standard [Production: ??? (SO)] 
Actual [Production: ??? (AO)] 

Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Quantity (kgs) 
Price Rs/kg 
Value/Cost (Rs) 
Material X 
2,266.67 
10 
22,667 
2,400 
11 
26,400 
Material Y 
1,511.11 
25 
37,778 
1,500 
24 
36,000 
Total
 3,777.78 

60,445 
3,900 

62,400 
Less: Loss @10%
 377.78 
1 
390 



Actual
 


500 


Net
 3,400 


3,400 


Using,
SP_{Mix} 
= 

⇒ SP_{Mix} 
= 

⇒ SP_{Mix} 
= 
Rs. 16/kg 
Using,
TMYV/TMSUV 
= 
(SL_{Mix} − AL_{Mix}) × SP_{Mix} 
• TMYV/TMSUV 
= 
(377.78 kgs − 500 kgs) × Rs. 16/kg 

= 
(− 122.12 kgs) × Rs. 16/kg 

= 
− Rs. 1,954 [Adv or Unf] 
It should have been 1,955.55 the difference being approximation error.


