Final answer:
Calculating the gross profit for ax Incorporated, we analyze two scenarios: one where units produced equals units sold, leading to a gross profit of $957,000, and another where more units are produced than sold, resulting in a higher gross profit of $1,226,400. The increase in gross profit from more production is $269,400.
Step-by-step explanation:
Calculating Gross Profit Under Absorption Costing
To compute the gross profit for ax Incorporated, we first need to calculate the total cost per unit. The total cost is comprised of direct materials, direct labor, variable overhead, and a portion of fixed overhead based on the number of units produced. Then we subtract the total cost from the sales revenue to calculate gross profit.
Scenario a: If 66,000 units are produced and sold, the entire fixed overhead is applied to these units. The cost per unit is:
- Direct Materials: $9.60
- Direct Labor: $7.10
- Variable Overhead: $11.60
- Fixed Overhead per Unit: $13.80 ($910,800 / 66,000 units)
Total Cost Per Unit = $42.10
Sales Revenue Per Unit = $56.60
Gross Profit Per Unit = Sales Revenue - Total Cost = $56.60 - $42.10 = $14.50
Total Gross Profit = Gross Profit Per Unit * Units Sold = $14.50 * 66,000 units = $957,000
Scenario b: If 92,000 units are produced but only 66,000 are sold, the fixed overhead per unit decreases because it is spread over more units. The new fixed overhead per unit is:
Fixed Overhead per Unit = $9.90 ($910,800 / 92,000 units)
Total Cost Per Unit = $38.20
Total Gross Profit = Gross Profit Per Unit * Units Sold = ($56.60 - $38.20) * 66,000 units = $1,226,400
The gross profit increases by the difference in gross profits between both scenarios.
Increase in Gross Profit = Gross Profit (Scenario b) - Gross Profit (Scenario a) = $1,226,400 - $957,000 = $269,400