Answer :
To calculate material variances, we need to consider several components: Material Cost Variance (MCV), Material Price Variance (MPV), Material Usage Variance (MUV), and Material Mix and Yield Variances. Here's a step-by-step approach to find these variances.
Standard Mix Proportions:
- Material A: 60%
- Material B: 40%
Standard Prices:
- Material A: Rs. 20 per kg
- Material B: Rs. 10 per kg
Actual Input and Prices:
- Material A: 105 kg at Rs. 20 per kg
- Material B: 95 kg at Rs. 9 per kg
Actual Output:
- Loss: 35 kg
- Output: 165 kg
Total Input: 200 kg
Normal Loss: 20% of 200 = 40 kg
Therefore, standard output should be 200 - 40 = 160 kg
Material Cost Variance (MCV):
[tex]MCV = (Standard Cost of Actual Output) - (Actual Cost)[/tex]
1. Calculate Standard Cost of Actual Output:
For 165 kg output, considering 80% of input (normal yield is 160 kg for 200 kg input),
Standard Input = [tex]\frac{165}{160} \times 200 = 206.25 \text{ kg of input}[/tex]
Material A = 60% of 206.25 = 123.75 kg
Material B = 40% of 206.25 = 82.5 kg
Standard cost of Material A = 123.75 \times 20 = Rs. 2,475
Standard cost of Material B = 82.5 \times 10 = Rs. 825
Total Standard Cost = Rs. 2,475 + Rs. 825 = Rs. 3,300
2. Actual Cost:
- Actual Cost of Material A = 105 \times 20 = Rs. 2,100
- Actual Cost of Material B = 95 \times 9 = Rs. 855
Actual Total Cost = Rs. 2,100 + Rs. 855 = Rs. 2,955
[tex]MCV = 3,300 - 2,955 = Rs. 345 \text{ (Favorable)}[/tex]
Material Price Variance (MPV):
[tex]MPV = \sum \left( (Standard Price - Actual Price) \times Actual Quantity \right)[/tex]
MPV for Material A = (20 - 20) \times 105 = Rs. 0
MPV for Material B = (10 - 9) \times 95 = Rs. 95
Total MPV = Rs. 95 (Favorable)
Material Usage Variance (MUV):
[tex]MUV = \sum \left( (Standard Quantity for Actual Output - Actual Quantity) \times Standard Price \right)[/tex]
MUV for Material A = (123.75 - 105) \times 20 = Rs. 375
MUV for Material B = (82.5 - 95) \times 10 = -Rs. 125
Total MUV = Rs. 375 - Rs. 125 = Rs. 250 (Favorable)
These calculated variances provide insights into the efficiency and cost control of materials in the production process for Sigma Ltd.
