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Standard cost data of a product manufactured by Beta Ltd. is as follows: - Standard Material per unit of output: 5 kg @ ₹20 per kg - Standard Labour per unit of output: 3 hours @ ₹30 per hour Actual results for the month of October 2024 for an actual output of 2,000 units: - Material consumed: 10,800 kg at a total cost of ₹2,05,200 - Labour hours paid and worked: 5,800 hours at a total cost of ₹1,85,600 Compute the following variances: 1. Material Cost Variance (MCV), Material Price Variance (MPV), Material Usage Variance (MUV) 2. Labour Cost Variance (LCV), Labour Rate Variance (LRV), Labour Efficiency Variance (LEV)

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Detailed Solution & Explanation

### **Step 1: Material Variances Computation**

1. **Standard Quantity for Actual Output (SQ)**:
SQ=2,000 units×5 kg=10,000 kgSQ=2\displaystyle \text{SQ} = 2,000  units\displaystyle \text{ units} ×\displaystyle \times 5  kg=10\displaystyle \text{ kg} = 10,000  kg\displaystyle \text{ kg}
Standard Price (SP)=₹20 per kgStandard Price (SP)\displaystyle \text{Standard Price (SP)} = ₹20  per kg\displaystyle \text{ per kg}
Standard Cost of Material=10,000×₹20=₹2,00,000Standard Cost of Material=10\displaystyle \text{Standard Cost of Material} = 10,000 ×\displaystyle \times ₹20 = ₹2,00,000

2. **Actual Material Details**:
Actual Quantity (AQ)=10,800 kgActual Quantity (AQ)=10\displaystyle \text{Actual Quantity (AQ)} = 10,800  kg\displaystyle \text{ kg}
Actual Price (AP)=₹2,05,20010,800=₹19 per kg\displaystyle \text{Actual Price (AP)} = \frac{₹2,05,200}{10,800} = ₹19  per kg\displaystyle \text{ per kg}
Actual Cost of Material=₹2,05,200Actual Cost of Material\displaystyle \text{Actual Cost of Material} = ₹2,05,200

3. **Variances**:
- **Material Price Variance (MPV)**:
MPV=AQ×(SP−AP)=10,800×(20−19)=₹10,800 (Favourable)MPV=AQ\displaystyle \text{MPV} = \text{AQ} ×\displaystyle \times (SP−AP\displaystyle \text{SP} - \text{AP}) = 10,800 ×\displaystyle \times (20 - 19) = ₹10,800  (Favourable)\displaystyle \text{ (Favourable)}
- **Material Usage Variance (MUV)**:
MUV=SP×(SQ−AQ)=20×(10,000−10,800)=₹16,000 (Adverse)MUV=SP\displaystyle \text{MUV} = \text{SP} ×\displaystyle \times (SQ−AQ\displaystyle \text{SQ} - \text{AQ}) = 20 ×\displaystyle \times (10,000 - 10,800) = ₹16,000  (Adverse)\displaystyle \text{ (Adverse)}
- **Material Cost Variance (MCV)**:
MCV=Standard Cost−Actual Cost=2,00,000−2,05,200=₹5,200 (Adverse)\displaystyle \text{MCV} = \text{Standard Cost} - Actual Cost=2\displaystyle \text{Actual Cost} = 2,00,000 - 2,05,200 = ₹5,200  (Adverse)\displaystyle \text{ (Adverse)}
*Verification: MPV+MUV=10,800 (F)+16,000 (A)=5,200 (A)=MCV\displaystyle MPV+MUV=10\displaystyle \text{MPV} + \text{MUV} = 10,800 (F)+16\displaystyle \text{ (F)} + 16,000 (A)=5\displaystyle \text{ (A)} = 5,200 (A)=MCV\displaystyle \text{ (A)} = \text{MCV}.*

### **Step 2: Labour Variances Computation**

1. **Standard Hours for Actual Output (SH)**:
SH=2,000 units×3 hours=6,000 hoursSH=2\displaystyle \text{SH} = 2,000  units\displaystyle \text{ units} ×\displaystyle \times 3  hours=6\displaystyle \text{ hours} = 6,000  hours\displaystyle \text{ hours}
Standard Rate (SR)=₹30 per hourStandard Rate (SR)\displaystyle \text{Standard Rate (SR)} = ₹30  per hour\displaystyle \text{ per hour}
Standard Labour Cost=6,000×₹30=₹1,80,000Standard Labour Cost=6\displaystyle \text{Standard Labour Cost} = 6,000 ×\displaystyle \times ₹30 = ₹1,80,000

2. **Actual Labour Details**:
Actual Hours (AH)=5,800 hoursActual Hours (AH)=5\displaystyle \text{Actual Hours (AH)} = 5,800  hours\displaystyle \text{ hours}
Actual Rate (AR)=₹1,85,6005,800=₹32 per hour\displaystyle \text{Actual Rate (AR)} = \frac{₹1,85,600}{5,800} = ₹32  per hour\displaystyle \text{ per hour}
Actual Labour Cost=₹1,85,600Actual Labour Cost\displaystyle \text{Actual Labour Cost} = ₹1,85,600

3. **Variances**:
- **Labour Rate Variance (LRV)**:
LRV=AH×(SR−AR)=5,800×(30−32)=₹11,600 (Adverse)LRV=AH\displaystyle \text{LRV} = \text{AH} ×\displaystyle \times (SR−AR\displaystyle \text{SR} - \text{AR}) = 5,800 ×\displaystyle \times (30 - 32) = ₹11,600  (Adverse)\displaystyle \text{ (Adverse)}
- **Labour Efficiency Variance (LEV)**:
LEV=SR×(SH−AH)=30×(6,000−5,800)=₹6,000 (Favourable)LEV=SR\displaystyle \text{LEV} = \text{SR} ×\displaystyle \times (SH−AH\displaystyle \text{SH} - \text{AH}) = 30 ×\displaystyle \times (6,000 - 5,800) = ₹6,000  (Favourable)\displaystyle \text{ (Favourable)}
- **Labour Cost Variance (LCV)**:
LCV=Standard Cost−Actual Cost=1,80,000−1,85,600=₹5,600 (Adverse)\displaystyle \text{LCV} = \text{Standard Cost} - Actual Cost=1\displaystyle \text{Actual Cost} = 1,80,000 - 1,85,600 = ₹5,600  (Adverse)\displaystyle \text{ (Adverse)}
*Verification: LRV+LEV=11,600 (A)+6,000 (F)=5,600 (A)=LCV\displaystyle LRV+LEV=11\displaystyle \text{LRV} + \text{LEV} = 11,600 (A)+6\displaystyle \text{ (A)} + 6,000 (F)=5\displaystyle \text{ (F)} = 5,600 (A)=LCV\displaystyle \text{ (A)} = \text{LCV}.*

Variance NameFormulaAmount (₹)Nature
Material Price Variance (MPV)AQ×(SP−AP)\displaystyle AQ ×\displaystyle \times (SP - AP)10,800Favourable
Material Usage Variance (MUV)SP×(SQ−AQ)\displaystyle SP ×\displaystyle \times (SQ - AQ)16,000Adverse
Material Cost Variance (MCV)StandardCost−ActualCost\displaystyle Standard Cost - Actual Cost5,200Adverse
Labour Rate Variance (LRV)AH×(SR−AR)\displaystyle AH ×\displaystyle \times (SR - AR)11,600Adverse
Labour Efficiency Variance (LEV)SR×(SH−AH)\displaystyle SR ×\displaystyle \times (SH - AH)6,000Favourable
Labour Cost Variance (LCV)StandardCost−ActualCost\displaystyle Standard Cost - Actual Cost5,600Adverse

Key Concepts to Understand

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