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Answer :
To calculate the material variance, we need to determine three components: the material price variance, the material usage variance, and the total material variance for each material type.
Step-by-step Calculation:
Material Price Variance (MPV):
The Material Price Variance is calculated using the formula:
[tex]\text{MPV} = (\text{Actual Price per Lb} - \text{Standard Price per Lb}) \times \text{Actual Usage for Output in Lb}[/tex]For Material A:
[tex]\text{MPV for A} = (12 - 10) \times 72 = 2 \times 72 = 144 \, \text{Rs}[/tex]For Material B:
[tex]\text{MPV for B} = (1 - 1) \times 108 = 0 \times 108 = 0 \, \text{Rs}[/tex]For Material C:
[tex]\text{MPV for C} = (4 - 5) \times 126 = -1 \times 126 = -126 \, \text{Rs}[/tex]
Material Usage Variance (MUV):
The Material Usage Variance is calculated using the formula:
[tex]\text{MUV} = (\text{Actual Usage for Output in Lb} - \text{Standard Usage for Output in Lb}) \times \text{Standard Price per Lb}[/tex]Calculate Standard Usage for each material:
- For Material A: [tex]\text{Standard Usage} = 36 \times 2 = 72 \, \text{Lb}[/tex]
- For Material B: [tex]\text{Standard Usage} = 36 \times 4 = 144 \, \text{Lb}[/tex]
- For Material C: [tex]\text{Standard Usage} = 36 \times 3 = 108 \, \text{Lb}[/tex]
For Material A:
[tex]\text{MUV for A} = (72 - 72) \times 10 = 0 \times 10 = 0 \, \text{Rs}[/tex]For Material B:
[tex]\text{MUV for B} = (108 - 144) \times 1 = -36 \times 1 = -36 \, \text{Rs}[/tex]For Material C:
[tex]\text{MUV for C} = (126 - 108) \times 5 = 18 \times 5 = 90 \, \text{Rs}[/tex]
Total Material Variance (TMV):
The Total Material Variance is the sum of the price and usage variances:
[tex]\text{TMV} = \text{MPV} + \text{MUV}[/tex]For Material A:
[tex]\text{TMV for A} = 144 + 0 = 144 \, \text{Rs}[/tex]For Material B:
[tex]\text{TMV for B} = 0 - 36 = -36 \, \text{Rs}[/tex]For Material C:
[tex]\text{TMV for C} = -126 + 90 = -36 \, \text{Rs}[/tex]
These calculations provide the variances attributed separately to price changes and usage efficiency for each material.
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