# Material Yield Variance

 A Problem
An output of 9,500 units is to be achieved using 900 kgs of Material A @ Rs. 15 per kg, 800 kgs of Material B @ Rs. 45/kg and 200 kgs of Material C @ Rs. 85 per kg. 22,800 units were actually manufactured using 2,250 kgs of Material A @ Rs. 16 per kg, 1,950 kgs of Material B @ Rs. 42/kg and 550 kgs of Material C @ Rs. 90 per kg.
The total quantity of materials used
As per Standard :: 900 kgs + 800 kgs + 200 kgs = 1,900 kgs.
Actually :: 2,250 kgs + 1,950 kgs + 550 kgs = 4,750 kgs.
What is the variation in total cost on account of variation in the output/yield achieved from the actual input?
This information is provided by the material yield variance.
The problem data arranged in a working table:

 Quantity(kgs) PriceRs/kg Value/Cost(Rs) Quantity(kgs) PriceRs/kg Value/Cost(Rs) Standard [Production: 9500 units] Actual [Production: 22,800 units] Material A 900 15 13,500 2,250 16 36,000 Material B 800 45 36,000 1,950 42 81,900 Material C 200 85 17,000 550 90 49,500 1,900 66,500 4,750 1,67,400

 The Formulae » Material Yield/Sub-Usage Variance (MYV/MSUV)
That part of the variance in the total cost of materials on account of a variation in the yield or output obtained from the materials used i.e. the standard output that should have been achieved for the actual input (i.e. AQMix) and the actual output/production/yield.

It is a part of the material Usage/Quantity Variance. It is a sub part of the Cost Variance. It is also called "Material Sub-Usage Variance" (MSUV).

It is the difference between the Standard Cost of Actual Output and the Standard Cost of Standard Output for Actual Input.
⇒ Material Yield/Sub-Usage Variance = Standard Cost of Actual Output − Standard Cost of Standard Output for Actual Input

• #### For each Material Separately

 This variance cannot be identified for each material separately.
• #### For all Materials together [Total Material Yield/Sub-Usage Variance :: TMY/TMSUV]

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

#### Note

The Material Yield Variance is calculated for all the materials together and cannot be used for each individual material.

This formula when applied for each material separately works as the alternative formula for Material Usage/Quantity Variance for each individual material.

 MYV/MSUV » Formula interpretation
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 Output to Standard Output for Actual Input.
• #### Standard − Actual or Actual − Standard??

Say the actual yield is 2,000 units and the standard yield for actual input is 1,800 units.
Does this indicate efficiency or inefficiency?
Efficiency for sure, since, 2,000 units have been produced with a resource to make 1,800 units.

This then should give us a positive variance. This would be possible only if we consider the data in the order "Actual" − "Standard". Be conscious of this, as in calculating all other material variances, we write "Standard" − "Actual".

• #### Where AQMix = SQMix

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

For each materials separately  There is no direct formula

For all the materials together  TMYV/TMSUV = (AO − SO) × SP(SO)

• #### TMYV/TMSUV = 0

The total Material Yield Variance would be zero, where the standard output for the actual input and the actual output are equal.

Where TMYV/TMSUV = 0, the total Material Usage/Quantity Variance is on account of Material Mix.  TMUV/TMQV = TMMV + TMYV/TMSUV = TMMV + 0 = TMMV

• #### TMYV/TMSUV = TMUV

The total Material Yield Variance would be equal to Total Material Usage/Quantity Variance where the Total Material Mix Variance is zero.  TMUV/TMQV = TMMV + TMYV/TMSUV = 0 + TMYV/TMSUV = TMYV/TMSUV

 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: 9500 units] Actual [Production: 22,800 units] Material A 900 15 13,500 2,250 16 36,000 Material B 800 45 36,000 1,950 42 81,900 Material C 200 85 17,000 550 90 49,500 1,900 66,500 4,750 1,67,400
Using,
SP(SO) =
 SCMix SO
• SP(SO) =
 Rs. 66,500 9,500 units
= Rs. 7/unit

TMYV =
(AO − {
 AQMix SQMix
× SO} ) × SP(SO)
Therefore, total Material yield Variance,
• TMYV/TMSUV =
(22,800 units − {
 4,750 1,900
× 9,500 units} ) × Rs. 7/unit
= (22,800 units − {2.5 × 9,500 units} ) × Rs. 7/unit
= (22,800 units − 23,750 units) × Rs. 7/unit
= (− 950 units) × Rs. 7/unit
= − Rs. 6,650 [Adv or Unf]

 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: 23,750 units] Actual [Production: 22,800 units] Material A 2,250 15 33,750 2,250 16 36,000 Material B 2,000 45 90,000 1,950 42 81,900 Material C 500 85 42,500 550 90 49,500 4,750 1,66,250 4,750 1,67,400
Using ,
SP(SO) =
 SCMix SO
=
 Rs. 1,66,250 23,750 units
= Rs. 7/unit
 ⇒ TMYV = (AO − SO) × SP(SO) = (22,800 units − 23,750 units) × Rs. 7/unit = (− 950 units) × Rs. 7/unit = − Rs. 6,650 [Adv]

#### 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.

 Formulae using Inter-relationships among Variances
1. MUV/MQV = MMV + MYV/MSUV
• #### For each Material Separately

 MYV/MSUVMat = MUV/MQVMat − MMVMat
• #### For All Materials Together

 TMYV/TMSUVMat = TMUV/TMQVMat − TMMVMat
2. MCV = MPV + MMV + MYV/MSUV
• #### For each Material Separately

 MYV/MSUVMat = MCVMat − MPVMat − MMVMat
• #### For All Materials Together

 TMYV/TMSUVMat = TMCVMat − TMPVMat − TMMVMat

#### Verification

The interrelationships between variances would also be useful in verifying whether our calculations are correct or not. After calculating all the variances we can verify whether
1. TMMV and TMYV add up to TMUV/TMQV or not. If we find it so, we can assume our calculations to be correct.
2. TMMV, TMYV and TMPV add up to TMCV or not. If we find it so, we can assume our calculations to be correct.

We used the same set of data in all the explanations. Using the figures obtained for verification.

 TMMV + TMYV/TMSUV = (− Rs. 2,000) + (− Rs. 6,650) = (− Rs. 8,650) = TMUV/TMQV → TRUE
 TMPV + TMMV +TMYV/TMSUV = (+ Rs. 850) + (− Rs. 2,000) + (− Rs. 6,650) = (− Rs. 7,800) = TMCV → TRUE

We can assume our calculations to be correct.

 Who is held responsible for the Variance?
 Since this variance is on account of more or less yield for the input used, the people or department responsible for producing the product (say manufacturing department) can be held responsible for this variance.

 Alternative Formula
The Total Material Yield/Sub-Usage Variance is the difference between the Standard Cost of Standard Materials for Actual Output and the Standard Cost of Actual Input.
Material Yield/Sub-Usage Variance
= Standard Cost of Standard Quantity for Actual Output − Standard Cost of Actual Quantity

• #### For each Material Separately

 This variance cannot be identified for each material separately.
• #### For all Materials together [Total Material Yield/Sub-Usage Variance :: TMY/TMSUV]

TMYV/TMSUV = SC of SQ for AO − SC of AQ
=
({  AO SO
× SQMix} × SPMix)
− (AQMix × SPMix)
=
({  AO SO
× SQMix} − AQMix) × SPMix)

#### Note

1. This formula can be used in all cases

#### Note

1. This formula when applied for each material separately is nothing but the formula for Material Usage/Quantity Variance for each individual material.
2. #### Standard − Actual (Or) Actual − Standard!!

Since the formula is based on inputs, it is Standard − Actual.
3. #### Where AO = SO

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

For each materials separately
 There is no direct formula

For all the materials together
 TMYV/TMSUV = (SQMix − AQMix) × SPMix

 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: 9500 units] Actual [Production: 22,800 units] Material A 900 15 13,500 2,250 16 36,000 Material B 800 45 36,000 1,950 42 81,900 Material C 200 85 17,000 550 90 49,500 1,900 66,500 4,750 1,67,400
Using,
SPMix =
 SCMix SQMix
• SPMix =
 Rs. 66,500 1,900 kgs
= Rs. 35/kg

Using
MYV/MSUV =
({
 AO SO
× SQMix} − AQMix) × SPMix
• MYV/MSUV =
({
 22,800 units 9,500 units
× 1,900 kgs} − 4,750 kgs) × Rs. 35/kg)
= ({2.4 × 1,900 kgs} − 4,750 kgs) × Rs. 35/kg)
= (4,560 kgs − 4,750 kgs) × Rs. 35/kg)
= (− 190 kgs) × Rs. 35/kg)
= − Rs. 6,650 [Adv]

 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 AO ≠ SO. Thus we recalculate the standard data for Actual Output [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: 22,800 units] Actual [Production: 22,800 units] Material A 2,160 15 32,400 2,250 16 36,000 Material B 1,920 45 86,400 1,950 42 81,900 Material C 480 85 40,800 550 90 49,500 4,560 1,59,600 4,750 1,67,400
Using
SPMix =
 SCMix SQMix
• SPMix =
 Rs. 1,59,600 4,560 kgs
= Rs. 35/kg
Using,
 MYV/MSUV = (SQMix} − AQMix) × SPMix)
 • MYV/MSUV = (4,560 kgs − 4,750 kgs) × Rs. 35/kg = (− 190 kgs) × Rs. 35/kg = − Rs. 6,650 [Adv]

 Author Credit : The Edifier ... Continued Page M:11

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