Material Variances :: Formula Review: Illustration

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Methodology » Approach

Arrange the data in a Working Table

Making a working table would form the first step for your problem solving effort.

True, your ability to solve problems on this topic is one way judged/decided by your ability to recollect the formulae. But, if you adopt the formulae that are capable of being used in all cases, it won't be difficult at all.

Yes, it would be very easy.

Your problem solving capability is limited by your ability to interpret the problem. If you notice all the examples we have given, the data in all the problems is structured (presented) in a similar manner, in the form of a table.

There lies the trick to make problem solving easy. Whatever may be the way the problem is presented (what we call problem models), get habituated to arranging the information in the form of a table as given below. Once you arrange that information, it would be very easy for you. Recollect the relevant formula and apply it.

If you try to understand the logic behind each formula, recollecting them also would be very easy. That is the reason we recommend the student to use the formula that is capable of being used in all cases.

Working table for arranging your data.

	Quantity (kgs)	Price Rs/kg	Value/Cost (Rs)	Quantity (kgs)	Price Rs/kg	Value/Cost (Rs)
	Standard [Production: SO]			Actual [Production: AO]
Material A	SQ_A	SP_A	SC_A	AQ_A	AP_A	AC_A
Material B	SQ_B	SP_B	SC_B	AQ_B	AP_B	AC_B
Material C	...	...	...	...	...	...
Total	SQ_Mix	SP_Mix	SC_Mix	AQ_Mix	AP_Mix	AC_Mix
Less: Loss @x%	SL_Mix			AL_Mix

There are two approaches to solving problems.

Using the given data as it is
If you use the formulae that are capable of being used in all situations, you just need to build the working table from the given data and things from thereon would be involving substituting data and evaluating the result.
This would be the best approach as all the adjustments you need to make with regard to the difference between the AO and SO as well as AQ_Mix and SQ_Mix would be taken care of within the formulae itself.
By Recalculating Standards where needed
If at all you wish to calculate variances by recalculating the standards, you have to recalculate the standards twice.
1. Once based on output (Standards for Actual Output) to ensure the condition SO = AO. The values for SQ and SO for calculating MCV and MUV/MQV should be considered from the working table ensuring this condition is satisfied.
2. The Second time based on input (Standards for Actual Input) to ensure the condition AQ_Mix = SQ_Mix. The values for SQ and SO for calculating MMV and MYV/MSUV should be considered from the working table ensuring this condition is satisfied.
All other values i.e. SP and the actual data (AP, AQ, AO) are not influenced by these conditions i.e., they would be the same in all cases.

Recommended Formulae!!!

The formulae that can be used in all situations should be used so that you would get accustomed to the formulae after doing some problems and would not be worried about not being able to recollect the correct formula.

Formulae that can be used in all cases

Material Cost Variance

⇒ MCV = ({
AO
SO
× SQ} × SP) − (AQ × AP)

Material Price Variance

⇒ MPV = (SP − AP) × AQ

Material Usage/Quantity Variance

⇒ MUV/MQV =
({
AO
SO
× SQ} − AQ) × SP

Material Mix Variance

⇒ MMV = ({
AQ_Mix
SQ_Mix
× SQ } − AQ) × SP

Material Yield/Sub-Usage Variance

⇒ MYV =
(AO − ({
AQ_Mix
SQ_Mix
× SO } × SP(SO) )

Standard Price of Output

SP(SO) =
SC_Mix
SO

Where

SQ = Standard Quantity of each Material

SO = Standard Output

SP = Standard Price of each Material

SQ_Mix = Standard Quantity of Mix

SC_Mix = Standard Cost of Mix

SP(SO) = Standard Price of Standard Output/Yield

SL_Mix = Standard Loss of Mix

AQ = Actual Quantity of each Material

AP = Actual Price of each Material

AO = Actual Output

AQ_Mix = Actual Quantity of Mix

AL_Mix = Actual Loss of Mix

Note :
If you understand the concept behind the variance, remembering the formula would not poce a problem at all. You may use the following tips to aid your effort (we feel even this should not be necessary for an average student).

Remember the simple formulae excluding the correction/adjustment factor in which case the formulae for MUV and MMV would be the same.

The SQ is to corrected/adjusted by a factor:

AO/SO for calculating the MCV and MUV/MQV

AQ_Mix/SQ_Mix for calculating MMV

The SO is to be corrected/adjusted by a factor

AQ_Mix/SQ_Mix for calculating MYV

MYV is dependent on "SO" and not "SQ".

Calculating Total Variances
Where there are two or more materials involved in the production process, total variances can be calculated as the sum of the variances for each material calculated separately using the above formulae.
MYV cannot be calculated for each material separately. Only TMYV/TMSUV can be calculated using the above formula.
TMCV variance can be calculated using a separate formula without requiring to calculate the individual variances.

A Problem

Three materials X, Y and Z are utilized in the manufacture of a product. The standard usage being 1,500 kgs of X @ Rs. 10/kg, 1,000 kgs of Y @ Rs. 12/kg and 500 kgs of Y @ Rs. 15/kg. The processing would result in a normal loss of materials @10% of total input quantity.
During a particular production period, the organisation has utilised 2,800 kgs of X purchased @ Rs. 11/kg, 2,100 kgs of Y purchased @ Rs. 11/kg and 600 kgs of Z purchased @ Rs. 16/kg for manufacture. The loss incurred was 12% of total input. Calculate all possible variances relating to materials.

Working Table

Working table incorporating the data in the problem

Standard
[Production: 2,700 kgs (SO)] Actual
[Production: 4,840 kgs (AO)]

Quantity
(kgs) Price
Rs/kg Value/Cost
(Rs) Quantity
(kgs) Price
Rs/kg Value/Cost
(Rs)

Material X 1,500 10 15,000 2,800 11 30,800

Material Y 1,000 12 12,000 2,100 11 23,100

Material X 500 15 7,500 600 16 9,600

Total 3,000 34,500 5,500 63,500

Less: Loss @10% 300

@12% 660

Output 2,700 4,840

Since the standard output and the actual output are not known, the information relating to losses is used to calculate the standard output and the actual output.

SO = SQ_Mix − SL_Mix ⇒ SO = 3,000 kgs − 300 kgs ⇒ SO = 2,700 kgs

AO = AQ_Mix − AL_Mix ⇒ AO = 5,500 kgs − 660 kgs ⇒ AO = 4,840 kgs

SP(SO) =
SC_Mix
SO
⇒ SP(SO) =
Rs. 34,500
2,700 kgs
⇒ SP(SO) = Rs.
115
9
/kg

The Solution

• Material Cost Variance [MCV]

MCV = ({
AO
SO
× SQ } × SP ) − (AQ × AP)

Using, MCV_Mat = ({
AO
SO
× SQ_Mat } × SP_Mat ) − (AQ_Mat × AP_Mat)

Material Cost Variance due to

• Material X =

({
4,840 units
2,700 units
× 1,500 kgs } × Rs. 10/kg ) − (2,800 kgs × Rs. 11/kg)

= Rs. 26,888.89 − Rs. 30,800

= − Rs. 3,911.11 ⇒ MCV_X = − Rs. 3,911.11 [Adv]

• Material Y =
({
4,840 units
2,700 units
× 1,000 kgs } × Rs. 12/kg ) − (2,100 kgs × Rs. 11/kg)

= Rs. 21511.11 − Rs. 23,100

= − Rs. 1,588.89 ⇒ MCV_B = − Rs. 1,588.89 [Adv]

• Material Z =
({
4,840 units
2,700 units
× 500 kgs } × Rs. 15/kg ) − (600 kgs × Rs. 16/kg)

= Rs. 13,444.44 − Rs. 9,600

= + Rs. 3,844.44 ⇒ MCV_C = + Rs. 3,844.44 [Fav]

Total Material Cost Variance ⇒ TMCV = − Rs. 1,655.56 [Adv]

• Material Price Variance [MPV]

MPV = (AQ × SP) − (AQ × AP) ⇒ MPV = AQ (SP − AP)
Using MPV_Mat = AQ_Mat (SP_Mat − AP_Mat)
Material Price Variance due to

• Material X = 2,800 kgs (Rs. 10/kg − Rs. 11/kg)

= 2,800 kgs (− Rs. 1/kg)

= − Rs. 2,800 ⇒ MPV_A = − Rs. 2,800 [Adv]

• Material B = 2,100 kgs (Rs. 12/kg − Rs. 11/kg)

= 2,100 kgs (Rs. 1/kg)

= + Rs. 2,100 ⇒ MPV_B = + Rs. 2,100 [Fav]

• Material C = 600 kgs (Rs. 15/kg − Rs. 16/kg)

= 600 kgs (− Rs. 1/kg)

= − Rs. 60 ⇒ MPV_C = − Rs. 600 [Adv]

Total Material Price Variance ⇒ TMPV = − Rs. 1,300 [Adv]

• Material Usage/Quantity Variance [MUV/MQV]

MUV/MQV =

({
AO
SO
× SQ} − AQ) × SP

Using, MUV/MQV_Mat =

({
AO
SO
× SQ_Mat} − AQ_Mat) × SP_Mat

Material Usage/Quantity Variance due to

• Material X =

({
4,840 units
2,700 units
× 1,500 kgs} − 2,800 kgs) × Rs. 10/kg

=
(
24,200 − 25,200
9
kgs) × Rs. 10/kg

= − Rs. 1,111.11 ⇒ MUV/MQV_X = − Rs. 1,111.11 [Adv]

• Material Y =

({
4,840 units
2,700 units
× 1,000 kgs} − 2,100 kgs) × Rs. 12/kg

=
(
48,400 − 56,700
27
kgs) × Rs. 12/kg

= − Rs. 3,688.89 ⇒ MUV/MQV_Y = − Rs. 3,688.89 [Adv]

• Material Z =

({
4,840 units
2,700 units
× 500 kgs} − 600 kgs) × Rs. 15/kg

=
(
24,200 − 16,200
27
kgs) × Rs. 15/kg

= − Rs. 4,444.44 ⇒ MUV/MQV_Z = − Rs. 4,444.44 [Adv]

Total Material Usage/Quantity Variance ⇒ TMUV/TMQV = − Rs. 355.56 [Adv]

• Material Mix Variance [MMV]

Using,

MMV =
({
AQ_Mix
SQ_Mix
× SQ_Mat} − AQ_Mat) × SP_Mat

Material Mix Variance due to

• Material X =
({
5,500 units
3,000 units
× 1,500 kgs} − 2,800 kgs) × Rs. 10/kg

= (2,750 kgs − 2,800 kgs) × Rs. 10/kg

= − 50 kgs × Rs. 10/kg

= − Rs. 500 ⇒ MMV_A = − Rs. 500 [Adv]

Material Y =
({
5,500 units
3,000 units
× 1,000 kgs} − 2,100 kgs) × Rs. 12/kg

=
(
5,500 − 6,300
3
kgs) × Rs. 12/kg

= − 3,200 ⇒ MMV_Y = − 3,200 [Adv]

Material Z =
({
5,500 units
3,000 units
× 500 kgs} − 600 kgs) × Rs. 15/kg

=
(
5,500 − 3,600
6
kgs) × Rs. 15/kg

= + Rs 4,750 ⇒ MMV_Z = + Rs 4,750 [Fav]

Total Material Mix Varaince ⇒ TMMV = − Rs. 1,050 [Fav]

• Material Yield Varaince [MYV]

Using

TMYV =
(AO − {

AQ_Mix
SQ_Mix
× SO} ) × SP(SO)

Therefore, total Material yield Variance,

• TMYV/TMSUV =
(4,840 units − {

5,500
3,000
× 2,700 units} ) × Rs.
115
9
/unit

=
(4,840 kgs − 4,950 kgs) × Rs.
115
9
/unit

= − Rs. 1,405.56 [Adv]

Verification

TMMV + TMYV/TMSUV = (+ Rs. 1,050) + (− Rs. 1,405.56)

= (− Rs. 355.56)

= TMUV/TMQV → TRUE

TMPV + TMMV +TMYV/TMSUV = (− Rs. 1,300) + (+ Rs. 1,050) + (− Rs. 1,405.56)

= (− Rs. 1,655.56)

= TMCV → TRUE

Wish to avoid approximation errors!!!
Consider as many places after the decimal as possible. The more places you consider, the lesser would be chance for error. This should not make you go crazily writing down numbers with long digits after the decimal. It would not be needed. One another method is to use fractions without writing them down in their decimal form, till you arrive at the last step. Say use Rs. 115/9 in place of Rs. 12.78 which would reduce the need for approximation to the greatest possible extent.
Caution
How does an amount of Rs. 123.45398723992873623212983439272 (Or) Rs. 143/7 sound......
Please, don't write your final figures as fractions or with more than two digits after the decimal. We are not in the science lab. We are talking of money.

Author Credit : The Edifier ... Continued Page M:13