Let's break down the requirements and solve the variances in **three steps** with explanations after each step, and provide the final answer at the end. --- ### **Step 1: Calculate Direct Materials Price and Quantity Variances** #### **Formulas:** - **Material Price Variance (MPV):** = (Actual Price - Standard Price) × Actual Quantity Purchased - **Material Quantity Variance (MQV):** = (Actual Quantity Used - Standard Quantity Allowed) × Standard Price #### **Details from the Problem:** - **Standard Price (SP):** $0.08/lb (asphalt) - **Actual Price (AP):** $0.09/lb (asphalt) - **Actual Quantity Purchased (AQP):** 765,000 lbs - **Actual Quantity Used (AQU):** 755,000 lbs - **Actual Output:** 500,000 shingles - **Standard Quantity Allowed (SQA):** 1.4 lbs/shingle × 500,000 = **700,000 lbs** #### **Calculations:** **Material Price Variance:** \[ MPV = (AP - SP) \times AQP = (\$0.09 - \$0.08) \times 765,000 = \$0.01 \times 765,000 = \$7,650 \] **Material Quantity Variance:** \[ MQV = (AQU - SQA) \times SP = (755,000 - 700,000) \times \$0.08 = 55,000 \times \$0.08 = \$4,400 \] #### **Explanation for Step 1:** - **MPV** evaluates if you paid more or less per pound of asphalt than expected. - **MQV** evaluates if you used more or less asphalt than planned for the actual number of shingles produced. --- ### **Step 2: Calculate Direct Labor Rate and Efficiency Variances** #### **Formulas:** - **Labor Rate Variance (LRV):** = (Actual Rate - Standard Rate) × Actual Hours Worked - **Labor Efficiency Variance (LEV):** = (Actual Hours Worked - Standard Hours Allowed) × Standard Rate #### **Details from the Problem:** - **Standard Rate (SR):** $8.00/hr - **Actual Rate (AR):** $9.00/hr - **Actual Hours Worked (AHW):** 5,300 hrs - **Standard Hours Allowed (SHA):** 0.01 hr/shingle × 500,000 = **5,000 hrs** #### **Calculations:** **Labor Rate Variance:** \[ LRV = (AR - SR) \times AHW = (\$9.00 - \$8.00) \times 5,300 = \$1.00 \times 5,300 = \$5,300 \] **Labor Efficiency Variance:** \[ LEV = (AHW - SHA) \times SR = (5,300 - 5,000) \times \$8.00 = 300 \times \$8.00 = \$2,400 \] #### **Explanation for Step 2:** - **LRV** evaluates if workers were paid more or less per hour than planned. - **LEV** evaluates if more or fewer hours were worked than allowed for the output achieved. --- ### **Step 3: Variable Overhead Spending and Efficiency Variances** #### **Formulas:** - **Variable Overhead Spending Variance (VOSV):** = (Actual VOH Rate - Standard VOH Rate) × Actual Hours Worked - **Variable Overhead Efficiency Variance (VOEV):** = (Actual Hours Worked - Standard Hours Allowed) × Standard VOH Rate #### **Details from the Problem:** - **Standard VOH Rate:** $2/hr - **Actual VOH Incurred:** $11,230 - **Actual Hours Worked:** 5,300 hrs - **Standard Hours Allowed:** 5,000 hrs **Actual VOH Rate = $11,230 / 5,300 = $2.12/hr** #### **Calculations:** **Variable Overhead Spending Variance:** \[ VOSV = (Actual VOH Rate - Standard VOH Rate) \times Actual Hours Worked = (2.12 - 2.00) \times 5,300 = 0.12 \times 5,300 = \$636 \] **Variable Overhead Efficiency Variance:** \[ VOEV = (Actual Hours Worked - Standard Hours Allowed) \times Standard VOH Rate = (5,300 - 5,000) \times 2.00 = 300 \times 2.00 = \$600 \] #### **Explanation for Step 3:** - **VOSV** evaluates if the variable overhead cost per hour was more or less than budgeted. - **VOEV** evaluates if more or fewer hours were worked than allowed, impacting variable overhead. --- ## **Final Answer** ### **Step-by-Step Variances:** **1. Direct Materials:** - **Material Price Variance:** $7,650 - **Material Quantity Variance:** $4,400 **2. Direct Labor:** - **Labor Rate Variance:** $5,300 - **Labor Efficiency Variance:** $2,400 **3. Variable Manufacturing Overhead:** - **Spending Variance:** $636 - **Efficiency Variance:** $600 --- ### **Pick Two Variances to Investigate & Possible Causes** **1. Material Price Variance ($7,650):** - **Reason to investigate:** Largest dollar amount. Indicates purchasing asphalt at a higher price than standard. - **Possible cause:** Supplier price increases, rush orders, lower quality, or purchasing department inefficiencies. **2. Labor Rate Variance ($5,300):** - **Reason to investigate:** Significant variance. Indicates workers were paid more per hour than expected. - **Possible cause:** Overtime, hiring more skilled workers, labor market changes, or errors in payroll. --- **Summary Table:** | Variance | Amount | Possible Cause | |------------------------------------|----------|----------------------------------------| | Material Price Variance | $7,650 | Supplier prices, purchasing issues | | Material Quantity Variance | $4,400 | Waste, inefficiency, spoilage | | Labor Rate Variance | $5,300 | Overtime, higher skilled labor | | Labor Efficiency Variance | $2,400 | Worker efficiency, machine downtime | | Variable Overhead Spending Variance| $636 | Utility rates, indirect materials cost | | Variable Overhead Efficiency Var. | $600 | Over/under usage of labor hours | --- **Final Answer:** The two variances that should be investigated are the **Material Price Variance ($7,650)** and the **Labor Rate Variance ($5,300)** due to their size and potential impact. The possible causes are supplier price changes, purchasing inefficiencies, overtime, or higher labor rates than planned.