Mazeppa Corporation sells relays at a selling price of $28 per unit. The company's cost per unit, based on full capacity of 160,000 units, is as follows: Direct materials $6
Direct labor 4
Overhead (2/3 of which is variable) 9

Mazeppa has been approached by a distributor in Montana offering to buy a special order consisting of 30,000 relays. Mazeppa has the capacity to fill the order. However, it will incur an additional shipping cost of $2 for each relay it sells to the distributor.

Required:
a. Assume that Mazeppa is currently operating at a level of 100,000 units. Show the calculation for the unit price to charge the distributor which will generate an increase in operating income of $2 per unit.
b. Assume that Mazeppa is currently operating at full capacity. To fill the special order, regular customers will have to be turned away. Now what unit price should it charge the distributor if it wishes to increase total operating income by $60,000 more than it would be without accepting the special order?

a. $20.00

b. $28,75

Explanation:

Find the total incremental costs to satisfy the special order and add $2.00 profit (because we are aiming for a profit not to just break-even).

Calculation of Total Incremental Unit Costs

Direct materials                                          $6 .00

Direct labor                                                 $4.00

Variable Overheads (2/3 × $9)                  $6.00

Shipping Cost                                             $2.00

Total Incremental Unit Cost                      $18.00

Add Profit Element                                     $2.00

Unit Selling Price for the Special Order  $20.00

In this case no changes will occur on fixed overheads, hence it is irrelevant.

Calculation of Desired Net Operating Income

Sales ($28 × 160,000 units)                                     $4,480,000

Less Product Costs :

Direct materials ($6 .00 × 160,000 units)                 ($960,000)

Direct labor ($4.00 × 160,000 units)                        ($640,000)

Variable Overheads ($6.00 × 160,000 units)          ($960,000)

Fixed Overheads ($3.00 × 160,000 units)               ($480,000)

Current Operating Income                                       $1,440,000

Add Desired Increase in Operating Income               $60,000

Desired Operating Income                                      $1,500,000

Unit Profit = $1,500,000 ÷ 160,000 units

                  = $9.375

Unit Profit = Unit Selling Price - Total Unit Costs - Unit Incremental Profit

therefore,

Unit Selling Price = Unit Profit  + Total Unit Costs + Unit Incremental Profit

                             = $9.375 + $19.00 + $0.375

                             = $28,75