William Company owns and operates a nationwide chain of movie theaters. The 500 properties in the William chain vary from low volume, small town, single-screen theaters to high volume, big city, multi-screen theaters. The management is considering installing machines that will make popcorn on the premises. These machines would allow the theaters to sell popcorn that would be freshly popped daily rather than the pre-popped corn that is currently purchased in large bags. This proposed feature would be properly advertised and is intended to increase patronage at the company's theaters. Annual rental costs and operating costs vary with the size of the machines. The machine capacities and costs are as follows:

Economy Regular Super
Annual capacity (boxes) Cost 50,000 120,000 300,000
Annual machine rental $8,000 $11,000 $20,000
Popcorn cost per box 130 130 130
Other costs per box 220 140 050
Cost of each box 080 080 080

Required:
a. Calculate the volume level in boxes at which the economy popper and regular popper would earn the same profit (loss).
b. Management can estimate the number of boxes to be sold at each of its theaters. Present a decision rule that would enable William's management to select the most profitable machine without having to make a separate cost calculation for each theater.
c. Could management use the average number of boxes sold per seat for the entire chain and the capacity of each theater to develop this decision rule? Explain your answer.

William Company

a) Volume level in boxes at which the economy popper and the regular popper would earn the same profit (loss):

                                                  Economy       Regular     Difference in costs

Total Fixed costs                       $58,000      $131,000     $73,000

Total Variable costs per unit    $430            $350           $80

Volume = Difference in fixed costs/Difference in variable = $73,000/$80

= 912.5 boxes

b. Decision rule:  We assume a selling price of $1,000 per box, then based on this selling price, we calculate the contribution per box.  The decision rule is to purchase the machine that has the least break-even point in sales unit.

                                                  Economy          Regular          Super

Total fixed annual costs            $58,000        $131,000     $320,000

Selling price per box                    $1,000           $1,000           $1,000

Total variable cost per box            $430              $350             $260

Contribution per box                     $570              $650             $740

Break-even point =                       101.75            201.54          432.43

The most profitable machine is the Economy Popper since it has the least break-even point.  This is the point at which management will start realizing some profits after covering all the fixed costs.

c. Management may not be able to use the average number of boxes sold per seat for the entire chain and the capacity of each theater to develop this decision rule.  Using this will be complicated.  But, using the break-even point for each machine is a lot easier and simpler to implement.

Explanation:

a) Machine Capacities and Costs Data and Calculations:

                                                  Economy          Regular          Super

Annual capacity (boxes) Cost     50,000          120,000        300,000

Annual machine rental                $8,000           $11,000       $20,000

Total fixed annual costs            $58,000        $131,000     $320,000

Popcorn cost per box                        130                  130                130

Other costs per box                         220                  140               050

Cost of each box                              080                 080               080

Total variable cost per box            $430              $350             $260