# Material Yield Variance : Losses

 Losses
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

 ⇒ AO = AQMix − ALMix

• Standard Output = Standard Quantity of Standard Mix − Standard Loss

 ⇒ SO = SQMix − SLMix

#### 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 SCMix 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:

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: ???] Actual [Production: ???] Material X 500 10 5,000 470 11 5,170 Material Y 700 25 17,500 700 24 16,800 1,200 22,500 1,170 21,970 120 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 = AQMix − ALMix  • AO = 1,170 kgs − 110 kgs = 1,060 kgs
• Using, SO = SQMix − SLMix  • 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.

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: 1,080 kg] Actual [Production: 1,060 kg] Material X 500 10 5,000 470 11 5,170 Material Y 700 25 17,500 700 24 16,800 1,200 22,500 1,170 21,970 120 10 1,200 110 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).

SP(SO) =  SCMix SQMix

You would be required to calculate the "Standard Price of Output" SP(SO), for which you need the "Standard Cost of Mix" SCMix. 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.]

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: 2000 units] Actual [Production: 1800 units] Material X 500 10 5,000 470 11 5,170 Material Y 700 25 17,500 700 24 16,800 1,200 22,500 1,170 21,970 120 10 1,200 110 – 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.

SP(SO) =  SCMix SQMix

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

TMYV/TMSUV = SC of SLMix for AQMix − SC of ALMix
=
({
 AQMix SQMix
× SLMix} × SP(SO)) − (ALMix × SP(SO))
=
({
 AQMix SQMix
× SLMix} − ALMix) × SP(SO)

#### Note:

This formula can be used in all cases i.e. both when AQMix = SQMix as well as when AQMix ≠ SQMix. When AQMix ≠ SQMix, AQMix/SQMix works as an adjustment factor to readjust the Standard to Standard for Actual Input.
• #### When AQMix = SQMix

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

In such a case, the formula would read  TMYV/TMSUV = (SLMix − ALMix) × 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:

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: ??? (SO)] Actual [Production: ??? (AO)] Material X 1,500 10 15,000 2,400 11 26,400 Material Y 1.000 25 25,000 1,500 24 36,000 2,500 40,000 3,900 62,400 250 1 250 500 2,250 3,400

Since the output data is not given, we calculate output from the given data.

Using,
 SO = SQMix − SLMix ⇒ SO = 2,500 kgs − 250 kgs ⇒ SO = 2,250 kgs

Using,
 AO = AQMix − ALMix ⇒ AO = 3,900 kgs − 500 kgs ⇒ AO = 3,400 kgs

Using
SP(SO) =
 SCMix SO
⇒ SP(SO) =
 Rs. 40,000 2,250 kgs
⇒ SP(SO) =
Rs.
 160 9
/kg

Using,
TMYV/TMSUV =
({
 AQMix SQMix
× SLMix} − ALMix) × SP(SO)
• TMYV/TMSUV =
({
 3,900 kgs 2,500 kgs
× 250 kgs} − 500 kgs) × Rs.
 160 9
/kg
=
(390 kgs − 500 kgs) × Rs.
 160 9
/kg
=
(− 110 kgs) × Rs.
 160 9
/kg

#### Check:

MYV using the formula for output,
MYV =
(AO − {
 AQMix SQMix
× SO}) × SP(SO)
• TMYV/TMSUV =
(3,400 − {
 3,900 kgs 2,500 kgs
× 2,250}) × Rs.
 160 9
/kg
=
(3,400 kgs − 3,510 kgs) × Rs.
 160 9
/kg
=
(− 110 kgs) × Rs.
 160 9
/kg

 Solution [Using recalculated data]
Where you find that the SQMix ≠ AQMix, you may alternatively recalculate the standard to make the SQMix = AQMix 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 AQMix/SQMix).

From the data relating to the problem, it is evident that SQMix ≠ AQMix. 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.

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: ??? (SO)] Actual [Production: ??? (AO)] Material X 2,340 10 23,400 2,400 11 26,400 Material Y 1.560 25 39,000 1,500 24 36,000 3,900 62,400 3,900 62,400 390 1 390 500 3,510 3,400

Since the output data is not given, we calculate output from the given data.

Using,
 SO = SQMix − SLMix ⇒ SO = 3,900 kgs − 390 kgs ⇒ SO = 3,510 kgs

Using,
 AO = AQMix − ALMix ⇒ AO = 3,900 kgs − 500 kgs ⇒ AO = 3,400 kgs

Using
SP(SO) =
 SCMix SO
⇒ SP(SO) =
 Rs. 62,400 3,510 kgs
⇒ SP(SO) =
Rs.
 160 9
/kg

Using,
 TMYV/TMSUV = (SLMix − ALMix) × SP(SO)

• TMYV/TMSUV =
(390 kgs − 500 kgs) × Rs.
 160 9
/kg
=
(− 110 kgs) × Rs.
 160 9
/kg

#### Check:

MYV using the formula for output,
MYV =
(AO − {
 AQMix SQMix
× SO}) × SP(SO)
• TMYV/TMSUV =
(3,400 − {
 3,900 kgs 2,500 kgs
× 2,250}) × Rs.
 160 9
/kg
=
(3,400 kgs − 3,510 kgs) × Rs.
 160 9
/kg
=
(− 110 kgs) × Rs.
 160 9
/kg

#### Note:

This formula can be used only when AQMix = SQMix.

#### You don't need to recalculate the standard

The formula with the adjustment factor AQMix/SQMix can be used in all cases i.e. both when AQMix = SQMix and AQMix ≠ SQMix. 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 AQMix = SQMix.

 Alternative Formula
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

MYV = SC of SL for AO − SC of AL
=
({
 AO SO
× SLMix} × SPMix) − (ALMix × SPMix)
=
({
 AO SO
× SLMix} − ALMix) × SPMix

#### 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 = (SLMix − ALMix) × SPMix

• #### 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:

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: ??? (SO)] Actual [Production: ??? (AO)] Material X 1,500 10 15,000 2,400 11 26,400 Material Y 1.000 25 25,000 1,500 24 36,000 2,500 40,000 3,900 62,400 250 1 250 500 2,250 3,400

Using,
SPMix =
 SCMix SQMix
⇒ SPMix =
 Rs. 40,000 2,500 kgs
⇒ SPMix = Rs. 16/kg

Using,
TMYV/TMSUV =
({
 AO SO
× SLMix} − ALMix) × SPMix
• TMYV/TMSUV =
({
 3,400 kgs 2,250 kgs
× 250 kgs} − 500 kgs) × Rs. 16/kg
=
({
 3,400 9
kgs} − 500 kgs) × Rs. 16/kg
=
({
 3,400 − 4,500 kgs 9
) × Rs. 16/kg
=
({
 − 1,100 kgs 9
) × 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.

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: ??? (SO)] Actual [Production: ??? (AO)] 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 3,777.78 60,445 3,900 62,400 377.78 1 390 500 3,400 3,400

Using,
SPMix =
 SCMix SQMix
⇒ SPMix =
 Rs. 60,445 3,777.78 kgs
⇒ SPMix = Rs. 16/kg

Using,
 TMYV/TMSUV = (SLMix − ALMix) × SPMix
 • 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.

 Author Credit : The Edifier ... Continued Page M:12