Pinnocle Corporation has provided the following data from its activity-based costing system: Activity Cost PoolTotal CostTotal Activity Assembly$1,363,440 69,000machine-hours Processing orders 45,254 1,700orders Inspection 120,754 1,730inspection-hours The company makes 490 units of product S78N a year, requiring a total of 740 machine-hours, 30 orders, and 10 inspection-hours per year. The product's direct materials cost is $50.61 per unit and its direct labor cost is $12.74 per unit. The product sells for $116.40 per unit. According to the activity-based costing system, the product margin for product S78N is:

Contribution margin = $20.15

Explanation:

First, we need to calculate the estimated overhead rate for each activity cost pool.

To calculate the estimated manufacturing overhead rate we need to use the following formula:

Estimated manufacturing overhead rate = total estimated overhead costs for the period / total amount of allocation base

Assembly = 1,363,440/69,000 = $19.76 per machine-hour

Processing orders = 45,254/1,700 = $26.62 per order

Inspection = 120,754/1,730 = $69.8

Now, we need to allocate overhead to S78 N units:

Allocated MOH = Estimated manufacturing overhead rate * Actual amount of allocation base

Assembly = 19.76*740 hours = 14,622.4

Processing = 26.62*30 = 798.6

Inspection = 69.8*10 = 698

Total = $16,119

Unitary overhead = 16,119/490 = $32.90

Finally, we can calculate the unitary cost and product margin:

Total unitary cost = direct material + direct labor + allocated overhead

Total unitary cost = 50.61 + 12.74 + 32.90 = $96.25

Contribution margin = selling price - total unitary cost

Contribution margin = 116.4 - 96.25 = $20.15