Let's break down the step by step both requirements (a) and (b): --- ## **a. ConventionalDirect Labor-Hour) Method** **Step 1: Calculate Total Direct Labor-Hours** - **Product A:** \( 22,000 \text{ units} \times 1.5 \text{ hours/unit} = 33,000 \text{ hours} \) - **Product B:** \( 5,500 \text{ units} \times 3 \text{ hours/unit} = 16,500 \text{ hours} \) - **Total Direct Labor-Hours:** \( 33,000 + 16,500 = 49,500 \text{ hours} \) --- ### **Step 2: Calculate Predetermined Overhead Rate** \[ \text{Overhead Rate} = \frac{\text{Total Estimated Overhead}}{\text{Total Direct Labor-Hours}} = \frac{\$396,000}{49,500 \text{ hours}} = \$8/\text{DLH} \] --- ### **Step 3: Allocate Overhead to Each Product** - **Product A:** \( 1.5 \text{ hours/unit} \times \$8 = \$12 \) overhead per unit - **Product B:** \( 3 \text{ hours/unit} \times \$8 = \$24 \) overhead per unit --- ### **Step 4: Calculate Total Unit Product Cost** #### **Product A:** - Direct Material: \$9 - Direct Labor: \$7 - Overhead: \$12 **Total: \$28** #### **Product B:** - Direct Material: \$20 - Direct Labor: \$15 - Overhead: \$24 **Total: \$59** --- ## **b. Activity-Based Costing (ABC) Method** ### **Step 1: Calculate Cost Driver Rates** - **Machine Setups:** \( \$170,000 / 1,700 = \$100 \) per setup - **Purchase Orders:** \( \$37,000 / 500 = \$74 \) per order - **Machine-Hours:** \( \$91,000 / 13,000 = \$7 \) per machine-hour - **Maintenance Requests:** \( \$98,000 / 1,000 = \$98 \) per request --- ### **Step 2: Assign Overhead to Each Product** #### **Product A:** - Machine Setups: \( 700 \times \$100 = \$70,000 \) - Purchase Orders: \( 300 \times \$74 = \$22,200 \) - Machine-Hours: \( 4,000 \times \$7 = \$28,000 \) - Maintenance Requests: \( 400 \times \$98 = \$39,200 \) - **Total Overhead for Product A:** \( \$70,000 + \$22,200 + \$28,000 + \$39,200 = \$159,400 \) - **Overhead per Unit A:** \( \$159,400 / 22,000 = \$7.245 \approx \$7.25 \) #### **Product B:** - Machine Setups: \( 1,000 \times \$100 = \$100,000 \) - Purchase Orders: \( 200 \times \$74 = \$14,800 \) - Machine-Hours: \( 9,000 \times \$7 = \$63,000 \) - Maintenance Requests: \( 600 \times \$98 = \$58,800 \) - **Total Overhead for Product B:** \( \$100,000 + \$14,800 + \$63,000 + \$58,800 = \$236,600 \) - **Overhead per Unit B:** \( \$236,600 / 5,500 = \$43.018 \approx \$43.02 \) --- ### **Step 3: Calculate Total Unit Product Cost (ABC)** #### **Product A:** - Direct Material: \$9 - Direct Labor: \$7 - Overhead: \$7.25 **Total: \$23.25** #### **Product B:** - Direct Material: \$20 - Direct Labor: \$15 - Overhead: \$43.02 **Total: \$78.02** --- ## **Summary Table** | Product | Method | Direct Material | Direct Labor | Overhead | Total Unit Cost | |-----------|---------------|----------------|--------------|----------|-----------------| | Product A | Conventional | $9 | $7 | $12 | $28.00 | | Product B | Conventional | $20 | $15 | $24 | $59.00 | | Product A | ABC | $9 | $7 | $7.25 | $23.25 | | Product B | ABC | $20 | $15 | $43.02 | $78.02 | --- ### **Final Answers** - **Conventional Method:** - Product A: **\$28.00** per unit - Product B: **\$59.00** per unit - **ABC Method:** - Product A: **\$23.25** per unit - Product B: **\$78.02** per unit Let me know if you need a breakdown of calculations or further explanation on any step!

# Theory Behind Each Calculation Understanding the calculation methods used in cost accounting is essential for evaluating product costs accurately. Below is a theoretical overview of the two methods used: the Conventional Method (Direct Labor-Hour) and the Activity-Based Costing (ABC) Method. ## **1. Conventional Method (Direct Labor-Hour)** ### **Overview** This method allocates manufacturing overhead costs based on direct labor hours. This approach assumes that the amount of overhead incurred is directly proportional to the labor hours worked. ### **Key Steps Explained** #### **Step 1: Total Direct Labor-Hours** - **Calculation:** Multiply the units produced by hours required per unit. - **Theory:** This step provides the total time laborers spend on manufacturing, forming the basis for overhead allocation. #### **Step 2: Predetermined Overhead Rate** - **Calculation:** Divide total estimated overhead costs by total direct labor hours. - **Theory:** The overhead rate reflects the cost incurred for every hour of labor used in production. This rate is predetermined to facilitate budget planning. #### **Step 3: Allocate Overhead** - **Calculation:** Multiply the overhead rate by the direct labor hours for each product. - **Theory:** This allocation method ensures that each product bears a fair share of the overhead costs based on its labor intensity. #### **Step 4: Total Unit Product Cost** - **Calculation:** Sum direct materials, direct labor, and allocated overhead. - **Theory:** This step gives the total cost of producing one unit, which is vital for pricing strategies and profitability analysis. ## **2. Activity-Based Costing (ABC) Method** ### **Overview** ABC assigns overhead costs based on activities that consume resources, providing a more accurate cost per product by identifying the relationship between costs, activities, and products. ### **Key Steps Explained** #### **Step 1: Cost Driver Rates** - **Calculation:** Divide the total cost for each activity by the total number of cost drivers (like setups, orders, etc.). - **Theory:** This approach recognizes that not all products consume resources equally. It assigns costs based on actual usage of activities. #### **Step 2: Assign Overhead** - **Calculation:** Multiply the cost driver rate by the number of cost drivers for each product. - **Theory:** This step provides a more precise allocation of overhead based on specific activities related to each product. It highlights the complexity of production processes. #### **Step 3: Total Unit Product Cost** - **Calculation:** Add direct materials, direct labor, and allocated overhead from ABC. - **Theory:** The total cost reflects a more accurate picture of production costs by considering the activities that drive costs, leading to better decision-making in pricing and efficiency improvements. ## **Conclusion** Each method offers unique insights into cost management. The Conventional Method is simpler and easier to implement but may not reflect the true cost of production as accurately as the ABC method. ABC provides detailed insights into cost behavior and resource usage, which can inform strategic decisions about product pricing and resource allocation. Understanding these methods allows managers to choose the most appropriate costing approach based on their organizational needs.