Duncan Co. sells product P at a price of $38 a unit. The per-unit cost data are: direct materials $8, direct labour $10, and overhead $12 (25% fixed and 75% variable). Wolff has sufficient capacity to accept a special order for 40,000 units just received. Selling costs associated with this order would be $3 per unit.
At a selling price of $33 per unit, the operating income will:
A) Increase by $60,000
B) Increase by $80,000
C) Increase by $120,000
D) Increase by $160,000

Question

Quizplus · Accepted Answer

To calculate the operating income at the regular selling price of $38, we need to first calculate the total cost per unit:

Total Cost Per Unit = Direct Materials + Direct Labour + Overhead
Total Cost Per Unit = $8 + $10 + $12 = $30

Therefore, the profit per unit at the regular selling price will be:

Profit Per Unit = Selling Price - Total Cost Per Unit
Profit Per Unit = $38 - $30 = $8

To calculate the profit per unit at the special order selling price of $33, we need to add the selling cost of $3:

Profit Per Unit = Selling Price - Total Cost Per Unit - Selling Cost
Profit Per Unit = $33 - $30 - $3 = $0

This means that there will be no profit per unit at the special order selling price of $33.

However, the question is asking for the operating income, which is calculated as:

Operating Income = (Profit Per Unit x Units Sold) - Fixed Costs

At the regular selling price of $38, the operating income for 40,000 units would be:

Operating Income = ($8 x 40,000) - (0.25 x $12 x 40,000) - (0.75 x $12 x 40,000)
Operating Income = $320,000 - $120,000 - $360,000
Operating Income = -$160,000 (a loss)

At the special order selling price of $33, the operating income for 40,000 units would be:

Operating Income = ($0 x 40,000) - (0.25 x $12 x 40,000) - (0.75 x $12 x 40,000) - ($3 x 40,000)
Operating Income = -$480,000 - $120,000 - $360,000 - $120,000
Operating Income = -$1,080,000 (a bigger loss)

Therefore, decreasing the selling price from $38 to $33 will decrease the operating income by $120,000 - (-$160,000) = $280,000. However, the question is asking for the increase in operating income, so we need to reverse the sign and get the answer of $120,000 increase (Option C).

Duncan Co Sells Product P at a Price of $38 a a Unit