P 2-27: William Company

                                 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. multiscreen theaters. The management is considering installing machines that will make popcorn on the premises. These machines would allow the theaters to sell freshly popped popcorn rather than prepopped corn that is currently purchased in large bags. This new feature would be 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 capac- ities and costs are as follows: Economy Regular Super Annual capacity (boxes) 50.000 120.000 300.000 Costs Annual machine rental $8.000 $11.000 $20.000 Popcorn cost per box 13c 13c 13c Other costs per box 22c 14c 05c Cost of each box 08c 08c 08c 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. SOURCE: CMA adapted.

a.Consider;

The cost of economy machine: 

Cost = Fixed Cost + Variable Cost 

=8000+ (13+ 22+ 8)*x 

= 8000 + 43x 

Hence the cost of the economy machine is 8000 +43x. 

The cost of the Regular machine: 

Cost = Fixed Cost + Variable Cost 

=11000+ (13+14+8)*x 

=11000+35x 

Therefore the cost of the Regular machine is $11000 +35x.

To get the equal profits the cost from two machines will be the same. 

Then,

Cost of Economy Machine = Cost of Regular Machine 

8000+ 43cents * x= 11000 + 35cents * x 

43cents * x -35cents * x = 11000 -8000 

x= 37,500 

Hence at 37500 boxes, the cost and profits from both the machines shall be equal. 

Step-by-step explanation

b. 

From the above on 37500 boxes the cost of the economy machine and the regular machine comes to be equal. Since the variable cost of the economy machine is higher after 37500 use of economy machine will be expensive and regular machine will be preferred here. 

Cost comparison should be made for the regular and super machine so as to get the breakeven based on which decision can be made. 

Let the volume be 'y'. 

Present the cost of the super machine: 

Cost = Fixed Cost + Variable Cost 

=20000+ (13+ 5+8)*y 

= 20000 + 26y 

Hence the cost of the super machine is 20000 +26*y.

Let the volume be y. 

Present the cost of the Regular machine: 

Cost = Fixed Cost + Variable Cost 

=11000+ (13+14+8)*y

= 11000 +35y 

Therefore the cost of the Regular machine is 11000 +35*y. 

For equal profits the cost from two machines will be the same. 

Cost of Super Machine = Cost of Regular Machine 

20000 + 26cents * y = 11000+ 35cents * y 

35cents* y- 26cents * y = 20000 -11000 

y =100000 

Therefore at 100000 boxes, the cost and profits from both the machines shall be equal. 

It can be concluded that is the sales at a theatre is up to 37500 boxes than machine economy should be used. If the sales are between 37500 boxes up to 100000 boxes then machine regular should be used and above 100000 boxes super machine should be used.

c. Using a common machine based on average is not appropriate and will lead to higher costs.

The installation according to the average requirement is not recommended because the theatre varies from place to place. At some places, economy machine is more beneficial while at other places regular or super will be beneficial.