A large university with a total enrollment of about 50,000 students has offered Pepsi-Cola an exclusivity agreement, which would give Pepsi exclusive rights to sell its products at all University facilities for the next year and option for future years. In return, the University would receive 35% of the on campus revenues and an additional lump sum of $200,000 per year. Pepsi has been given two weeks to respond.

The management at Pepsi quickly reviews what it knows. The market for soft drinks is measured in terms of the equivalent of 12 ounce cans. Pepsi currently sells an average of 22,000 cans or their equivalents per week (over the 40 weeks of the year that the University operates). They can sell for an average of $.75 each. The cost including labor amounts to $.20 per can. That she is unsure of its market share but suspects it’s considerably less than 50%. A quick analysis reveals that if the current market share were 25% then with an exclusivity agreement Pepsi would sell 88,000 cans per week. Thus, annual sales would be 3,520,000 cans per year (calculated as 88,000 cans per week time 40 weeks). The gross revenue would be computed as follows:

Gross revenue equals 3,520,000 cans times $.75 revenue/can equal $2,640,000 this figure must be multiplied by 65% since the University would rake in 35% of the gross.

The 65% times $2,640,000 equals $1,716,000

the total cost of $.20 per can (or $704,000) and the annual payment to the University of $200,000 is subtracted to obtain the net profit:

net profit equals $1,716,000 $-704,000 $-200,000 equals $812,000

the current annual profit is:

current profit equal 40 weeks times 22,000 cans per week times $.55 per can equals $484,000

if the current market share is 25%, the potential gain from the agreement is:

$812,000 $-484,000 equals $328,000.

The only problem with this analysis is that Pepsi does not know how many soft drinks are sold weekly at the University. In addition, Coke is not likely to supply Pepsi with information about its sales, which together with Pepsi’s line of products constitutes virtually the entire market.

A recent graduate of a businessprogram believes that a surveyof the university students can supply the needed information. Accordingly, she organizes a survey that asked 500 students to keep track of the number of soft drinks purchased on campus over the next seven days. Perform a statistical analysis to extract the needed information from the data. Estimate with a 95% confidence the parameter that is at the core of the decision problem. Use the estimate to compute estimates of annual profit. Assume the Coke and Pepsi drinkers will be willing to buy either product in the absence of their first choice.

1. On the basis of maximizing profits from sales of soft drinks at the University, should Pepsi agree to the exclusivity agreement?

2. Write a report to the company’s executives describing your analysis.

Please find attached a word file with step by step explanations …

A step by step explanation and solution of the problem, using formula calculations as well as excel solution of the problem.