Material Variances :: Solution : Problems involving Two or More Materials : Stocks Losses

Problem 3

Steps for solving the problems:

  1. Build the working table
  2. Substitute data in formulae
  3. Calculate
  4. Derive the answer.
 The working table is constructed for you and the net answers given so that you would be able to do the rest of the problem as an exercise. If you still feel the need for verifying your calculations, expand the remaining solution using the link given.
All the problems can be solved using the same set of formulae. 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 Actual Loss 7  
Output 90   78  

Net Answers :

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

Solution » Working Table

Hint:

Working table with the given data

Standard
[Output : 90 kgs] 		Actual
[Output : 78 kgs]
Quantity
(kgs) 		Price
/Unit 		Value/Cost
 Quantity
(kgs) 		Price
/Unit 		Value/Cost
Material P 60 3 180 50 4 200
Material Q 40 7 280 35 6 210
Total 100   460 85   410
Less: Loss 10 – –      
Actual       7    
Net 90     78    

Assumptions:

  1. None
Net Answers
TMCV = − 11.33 ; MPV = − 15; MUV/MQV = + 3.67;
MMV = − 4 and MYV/MSUV = + 7.67;

Solution » Calculations

• Material Cost Variance

Total MCV = MCV due to Material P + MCV due to Material Q

We know MCV = ({
AO
SO
× SQ } × SP) − (AQ × AP)
⇒ MCV due to Material P
=
({
78 kgs
90 kgs
× 60 kgs } × 3/kg)
− (50 kgs × 4/kg)
=
({
39
45
× 60 kgs} × 3/kg) − (50 kgs × 4/kg)
= 156 − 200
= − 44 [Adv or Unf]
⇒ MCV due to Material Q
=
({
78 kgs
90 kgs
× 40 kgs } × 7/kg)
− (35 kgs × 6/kg)
=
({
39
45
× 40 kgs} × 7/kg) − (35 kgs × 6/kg)
= 242.67 − 210
= + 32.67 [Pos or Fav]

Therefore, Total MCV = (− 44) + (+ 32.67)
⇒ Total MCV = − 11.33

• Material Price Variance

Total MPV = MPV due to Material P + MPV due to Material Q

We know MPV = AQ (SP − AP)
Therefore,

MPV due to Material P = 50 kgs ( 3/kg − 4/kg)
= 50 kgs (− 1/kg)
= − 50 [Adv or Unf]
MPV due to Material Q = 35 kgs ( 7/kg − 6/kg)
= 35 kgs (+ 1/kg)
= + 35 [Pos or Fav]

Therefore, Total MPV = (− 50) + (+ 35)
⇒ Total MPV = − 15

• Material Usage Variance or Material Quantity Variance [MUV/MQV]

Total MUV/MQV = MUV/MQV due to Material P + MUV/MQV due to Material Q

We know, MUV/MQV =
({
AO
SO
× SQ} − AQ) × SP
MUV/MQV due to Material P
=
({
78 kgs
90 kgs
× 60 kgs} − 50 kgs) × 3/kg
=
({
39
45
× 60 kgs} − 50 kgs) × 3/kg
=
({
39 × 4
3
kgs} − 50 kgs) × 3/kg
=
(
156 − 150
3
kgs) × 3/kg
= (+ 6 kgs) × 1/kg
= + 6 [Pos or Fav]
MUV/MQV due to Material P
=
({
78 kgs
90 kgs
× 60 kgs} − 50 kgs) × 3/kg
=
({
39
45
× 40 kgs} − 35 kgs) × 7/kg
=
({
39 × 8
9
kgs} − 35 kgs) × 7/kg
=
(
312 − 315
9
kgs) × 7/kg
=
(
− 3
9
kgs) × 7/kg
=
−
7
3
= − 2.33 [Adv or Unf]
Therefore, Total MUV/MQV = (+ 6) + (− 2.33 )
⇒ Total MUV/MQV = + 3.67

Verification
TMCV = TMPV + TMUV/TMQV
⇒ (− 11.33) = (− 15) + (+ 3.67)
⇒ − 11.33 = − 11.33 [True]
Therefore, we can assume the values we calculated are correct.

• Material Mix Variance

Total MMV = MMV due to Material P + MMV due to Material Q

We know, MMV = ({
TQAM
TQSM
× SQ} − AQ) × SP
Therefore,
MMV due to Material P
=
({
85 kgs
100 kgs
× 60 kgs} − 50 kgs) × 3/kg
= ({0.85 × 60 kgs} − 50 kgs) × 3/kg
= (51 kgs − 50 kgs) × 3/kg
= (+ 1 kg) × 3/kg
= + 3 [Pos or Fav]
MMV due to Material Q
=
({
85 kgs
100 kgs
× 40 kgs} − 35 kgs) × 7/kg
= ({0.85 × 40 kgs} − 35 kgs) × 7/kg
= (34 kgs − 35 kgs) × 7/kg
= (− 1 kg) × 7/kg
= − 7 [Adv or Unf]
Therefore, Total MMV = (+ 3) + (− 7)
⇒ Total MMV = − 4

• Material Yield Variance

Material Yield Variance is calculated based on the total quantity of materials and is not calculated for each separately.
We know, SRY =
TSCM
SO
⇒ SRY =
460
90 kgs
=
46
9
/kg
MYV =
(AO − {
TQAM
TQSM
× SQ}) × SRY
=
(78 kgs − {
85 kgs
100 kgs
× 90 kgs}) ×
46
9
/kg
=
(78 kgs − {0.85 × 90 kgs}) ×
46
9
/kg
=
(78 kgs − 76.5 kgs) ×
46
9
/kg
=
+ 1.5 kgs ×
46
9
/kg
=
+
23
3
= + 7.67 [Pos or Fav]

Solution » Verification

TMUV/TMQV = TMMV + TMYV/MSUV

Using the above data we get,
(+ 3.67) = (− 4) + (+ 7.67)
⇒ + 3.67 = + 3.67 → TRUE.

TMCV = TMPV + TMMV + TMYV/MSUV

Using the above data we get,
(− 11.33) = (− 15) + (− 4) + (+ 7.67)
⇒ − 11.33 = − 11.33 → TRUE.

Practice Problems

01.

From the following information, calculate the variances:

Material Standard Actual
Quantity
kgs 		Price
/Unit 		Total
 Quantity
kgs 		Price
/Unit 		Total
Roll 500 6 3,000 460 5 2,300
Goll 400 3.75 1,500 550 3 1,650
Poll 300 3 900 400 2.80 1,120
Gross Input 1,200   5,400 1,440   5,070
Less:Loss of Production 120     360    
Yield 1,080     1,080    

Answers for Practice Exercise

TMCV = + 330; MPV = + 952.50; MUV/MQV = − 622.50;
MMV = + 457.50 and MYV/MSUV = − 1,080;
Author : The Edifier