1) Material Price Variance is given as 51,000(F)
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(Standard Price – Actual Price) X Actual Quantity = 51,000(F)
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Actual Price per kg of Material is found to be less than Standard Price per kg of Material by 10
i.e. If, standard price is x; then actual price is (x-10)
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Hence, [x-(x-10)] X Actual Quantity = 51,000
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or, (x-x+10) X Actual Quantity = 51,000
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Therefore, Actual Quantity = 51,000/10 = 5,100 (Required)
2) Actual cost is given = 7,14,000
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Cost is simply calculated by multiplying quantity with price per unit
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Hence, Actual Cost = Actual Quantity X Actual Price
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or, 7,14,000 = 5,100 (as calculated in step 1) X Actual Price
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Therefore, Actual Price = 7,14,000/5,100 = 140 (Required)
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As in step 1, If, standard price is x; then actual price is (x-10)
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Hence, x-10 = 140
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or, x = 140+10 = 150 i.e. standard price
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Standard price is calculated because we will need the same for calculating the Material Usage Variance.
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Material Usage Variance = (standard quantity – actual quantity) X standard price
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(Whenever any variance is to be multiplied by price, we always consider standard price since while calculating one factor, other factor has to be kept constant. If we take actual price, then price variance will also be included.)
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Hence, Material Usage Variance = (5000 – 5100) X 150 = 15000 (A) (Required)
3) Material Cost Variance = Material Price Variance + Material Usage Variance
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or, Material Cost Variance = 51000 (F) + 15000 (A) = 36000 (F) (Required)