Material Variances :: Problems and Solutions : Two or More Materials

Problem 1

From the following information, calculate the variances:
Material Standard Actual
Usage
kg. 		Rate
per kg. 		Total
 Usage
kg. 		Rate
per kg. 		Total
P 60 3 180 50 4 200
Q 40 7 280 35 6 210
Gross Input 100   460 85   410
Less: Normal loss   10 Less: Actual Loss 7  
Output 90     78  

Net Answers :

[MCV = − 280 ; MPV = − 380; MUV/MQV = − 100 ; MMV = 0; MYV/MSUV = − 100;]

Solution » Working Table

The given data arranged in the form of a working table
StandardActual
Quantity
(kg) 		Price
/Unit 		Value/Cost
 Quantity
(kg) 		Price
/Unit 		Value/Cost
[Production: 90 kgs (SO)] [Production: 78 kgs (AO)]
Material P 60 3 180 50 4 200
Material Q 40 7 280 35 6 210
Total 100   460 85   410
Less: Loss 10     7    
Output 90     78    
SP(SO) =
SCMix
SO
 ⇒ SP(SO) =
460
90 kgs
⇒ SP(SO) =
46
9
/kg

Assumptions:

  1. None

Formulae Review and Complete Illustration

Solution » Calculations

• Material Cost Variance

MCV =({
AO
SO
× SQ } × SP ) − (AQ × AP)
Using, MCVMat =({
AO
SO
× SQMat } × SPMat ) − (AQMat × APMat)
Material Cost Variance due to
• Material P =
({
78 kgs
90 kgs
× 60 kgs } × 3/kg ) − (50 kgs × 4/kg)
= 156 − 200
= − 44 ⇒ MCVP = − 44.00 [Fav]
• Material Q =
({
78 kgs
90 kgs
× 40 kgs } × 7/kg ) − (35 kgs × 6/kg)
= 242.67 − 210
= + 32.67 ⇒ MCVQ = + 32.67 [Fav]
Total Material Cost Variance ⇒ TMCV = − 11.33 [Adv]

• Material Price Variance

MPV = (AQ × SP) − (AQ × AP) ⇒ MPV = AQ (SP − AP)

Using MPVMat = AQMat (SPMat − APMat)

Material Price Variance due to

• Material P = 50 kgs ( 3/kg − 4/kg)
= 50 kgs (− 1/kg)
= − 50 ⇒ MPVP = − 50 [Adv]
• Material Q = 35 kgs ( 7/kg − 6/kg)
= 35 kgs (+ 1/kg)
= + 35 ⇒ MPVQ = + 35 [Fav]
Total Material Price Variance ⇒ TMPV = − 15 [Adv]

• Material Usage/Quantity Variance

MUV/MQV =
({
AO
SO
 × SQ} − AQ) × SP
Using, MUV/MQVMat =
({
AO
SO
 × SQMat} − AQMat) × SPMat

Material Usage/Quantity Variance due to

• Material P =
({
78 kgs
90 kgs
× 60 kgs} − 50 kilos) × 3/kgs
= (52 kgs − 50 kgs) × 3/kg
= + 6 ⇒ MUV/MQVP = + 6 [Fav]
• Material Q =
({
78 kgs
90 kgs
× 40 kgs} − 35 kilos) × 7/kgs
= (34.67 kgs − 35 kgs) × 7/kg
= − 2.33 ⇒ MUV/MQVQ = − 2.33 [Adv]
Total Material Usage/Quantity Variance ⇒ TMUV/TMQV = + 3.67 [Fav]

• Material Mix Variance

Using,

MMV =
({
AQMix
SQMix
× SQMat} − AQMat) × SPMat
Material Mix Variance due to
• Material P =
({
85 kgs
100 kgs
× 60 kgs} − 50 kgs) × 3/kg
= (51 kgs − 50 kgs) × 3/kg
= + 3 ⇒ MMVP = + 3 [Fav]
Material Q =
({
85 kgs
100 kgs
× 40 kgs} − 35 kgs) × 7/kg
= (34 kgs − 35 kgs) × 7/kg
= − 7 ⇒ MMVQ = − 7 [Adv]
Total Material Mix Varaince ⇒ TMMV = − 4 [Adv]

• Material Yield/Sub-Usage Variance

Using

TMYV =
(AO − {
AQMix
SQMix
 × SO} ) × SP(SO)
Therefore, total Material yield Variance,
• TMYV/TMSUV =
(78 kgs − {
85 kgs
100 kgs
× 90 kgs} ) ×
46
9
/kg
=
(78 kgs − 76.5 kgs) ×
46
9
/kg
= + 7.67 [Fav]

Solution » Verification

TMCV = TMPV + TMUV/MQV

Using the above data we get,
TMPV + TMUV/TMQV = (− 15) + (+ 3.67)
= − 11.33
= TMCV     ← TRUE

TMUV/TMQV = TMMV + TMYV/TMSUV

Using the above data we get,
TMMV + TMYV/TMSUV = (− 4) + (+ 7.67)
= + 3.67
= TMUV/TMQV     ← TRUE

TMCV = TMPV + TMMV + TMYV/MSUV

Using the above data we get,
TMPV + TMMV + TMYV/MSUV = (− 15) + (− 4) + (+ 7.67)
= − 11.33
= TMCV     ← TRUE
Credit : Prasanthi Guntupalli