High School

A company manufactures a single product. The standard mix is as follows:

- Material A: 60% at ₹20 per kg
- Material B: 40% at ₹10 per kg

Normal loss in production is 20% of input. Due to a shortage of Material A, the standard mix was changed.

The actual results for February 2001 were:

- Material A: 105 kg at ₹20 per kg
- Material B: 95 kg at ₹9 per kg
- Actual Output: 165 kg

Calculate the various material variances.

Answer :

To calculate the various material variances, we need to determine the standard quantities and costs, then compare them against the actuals. From the provided data, the standard and actual information is:

Standard Data:

  • Material A: 60% of the mix at ₹ 20 per kg
  • Material B: 40% of the mix at ₹ 10 per kg
  • Normal loss: 20% of input

Actual Data for February 2001:

  • Material A: 105 kg at ₹ 20 per kg
  • Material B: 95 kg at ₹ 9 per kg
  • Actual Output: 165 kg

Step-by-Step Calculation:

  1. Calculate Total Input and Standard Output:

    Total input = Material A (60%) + Material B (40%)

    Normal Output = Total Input - 20% Lodds

    Let the total input be [tex]x[/tex] kg.

    Given the actual output is 165 kg, which is 80% of the total input (because of 20% loss).

    [tex]0.8x = 165 \\
    x = \frac{165}{0.8} = 206.25 \text{ kg}[/tex]

  2. Calculate Standard Quantities of Materials:

    • Standard Quantity of Material A = 60% of 206.25 kg = 123.75 kg
    • Standard Quantity of Material B = 40% of 206.25 kg = 82.5 kg

  3. Calculate Actual Total Cost and Standard Total Cost:

    • Actual Cost:

      • Material A = 105 kg * ₹ 20/kg = ₹ 2100
      • Material B = 95 kg * ₹ 9/kg = ₹ 855
      • Total = ₹ 2100 + ₹ 855 = ₹ 2955

    • Standard Cost:

      • Material A = 123.75 kg * ₹ 20/kg = ₹ 2475
      • Material B = 82.5 kg * ₹ 10/kg = ₹ 825
      • Total = ₹ 2475 + ₹ 825 = ₹ 3300

  4. Calculate Variances:

    • Material Cost Variance (MCV):

      [tex]\text{MCV} = \text{Standard Cost} - \text{Actual Cost} = 3300 - 2955 = ₹ 345[/tex]

    • Material Price Variance (MPV):

      For Material A:
      [tex]\text{MPV(A)} = (\text{Standard Price} - \text{Actual Price}) \times \text{Actual Quantity} = (20 - 20) \times 105 = 0[/tex]

      For Material B:
      [tex]\text{MPV(B)} = (10 - 9) \times 95 = 95[/tex]
      Total MPV = [tex]0 + 95 = ₹ 95[/tex]

    • Material Usage Variance (MUV):

      For Material A:
      [tex]\text{MUV(A)} = (\text{Standard Quantity} - \text{Actual Quantity}) \times \text{Standard Price} = (123.75 - 105) \times 20 = 375[/tex]

      For Material B:
      [tex]\text{MUV(B)} = (82.5 - 95) \times 10 = -125[/tex]
      Total MUV = [tex]375 - 125 = ₹ 250[/tex]

In summary, the Material Cost Variance is ₹ 345 (favorable), the Material Price Variance is ₹ 95 (favorable), and the Material Usage Variance is ₹ 250 (favorable). These variances help in understanding cost control and efficiency differences from the expected standards.

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