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Sigma Ltd. manufactures a single product, the standard mix of which is:

Material A 60% at Rs. 20 per kg.
Material B 40% at Rs. 10 per kg.

Normal loss in production is 20% of input. Due to shortage of Material A, the standard mix was changed. Actual results for March, 1999 were:

Material A 105 kg. at Rs. 20 per kg.
Material B 95 kg. at Rs. 9 per kg.
Input 200 kg.
Loss 35 kg.
Output 165 kg.

Calculate all material variances.

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.

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Rewritten by : Barada