Argentina Partners is concerned about the possible effects of inflation on its operations. Presently, the company sells 68,000 units for $45 per unit. The variable production costs are $25, and fixed costs amount to $780,000. Production engineers have advised management that they expect unit labor costs to rise by 20 percent and unit materials costs to rise by 15 percent in the coming year. Of the $25 variable costs, 50 percent are from labor and 25 percent are from materials. Variable overhead costs are expected to increase by 25 percent. Sales prices cannot increase more than 10 percent. It is also expected that fixed costs will rise by 5 percent as a result of increased taxes and other miscellaneous fixed charges. The company wishes to maintain the same level of profit in real dollar terms. It is expected that to accomplish this objective, profits must increase by 5 percent during the year.

Compute the volume in units and the dollar sales level necessary to maintain the present profit level, assuming that the maximum price increase is implemented.

First of all lets compute profit per unit as per existing data which is as below:

Selling price=$45/unit

Variable production cost=$25/unit

Labour cost=$12.5/unit ($25*50%)

Material cost=$6.25/unit($25*25%)

Variable overhead cost=$6.25/unit($25*25%)

Fixed cost=$11.47/unit ($780,000/68000 units)

Profit=$8.53 ($45-$25-$11.47)

Now lets calculate profit based on certain changes

Selling price=$49.5/unit ($45*10%)(As stated in question that assume maximum price increase)

Variable production cost=$30/unit ($15+$7.1875+$7.8125)

Labour cost=$15/unit ($12.5*1.2) (Labour cost to be increased by 20%)

Material cost=$7.1875/unit($6.25*1.15) (Material cost to be increased by 15%)

Variable overhead cost=$7.8125/unit($6.25*1.25) (V.POH to be increased by 25%)

Profit=$8.9545 ($8.53*1.05) (As stated in question profit must be increased by 5%)

Fixed cost=$819,000 ($780,000*1.05) (Fixed cost to be increased by 5%)

Fixed cost per unit=$10.5455 ($8.9545+$30-$49.5) Reverse working

Lets calculate volume by fixed cost per unit formula

Volume in units = Fixed cost/Fixed cost per unit

                          =$819,000/$10.5455

                           =77,663.5 units

Sales value = $695,438.27 (77,663.5*$8.9545)