In the last few years, colleges and universities have signed exclusivity agreements with a variety of private companies. These agreements bind the university to sell that company’s products exclusively on the campus. Many of the agreements involve food and beverage firms. A large university with a total enrollment of about 50,000 students has offered Pepsi-Cola an exclusivity agreement that would give Pepsi exclusive rights to sell its products at all university facilities for the next year and an 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 2 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). The cans sell for an average of one dollar each. The costs, including labor, amount to $.30 per can. Pepsi is unsure of its market share but suspects it is considerably less than 50%. A quick analysis reveals that if its 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 × 40 weeks). The gross revenue would be computed as follows*:

Gross revenue = 3,520,000 cans × $1.00 revenue/can = $3,520,000

This figure must be multiplied by 65% because the university would rake in 35% of the gross. Thus, 65% × $3,520,000 = $2,288,000

The total cost of 30 cents per can (or $1,056,000) and the annual payment to the university of

$200,000 is subtracted to obtain the net profit:

Net profit = $2,288,000−$1,056,000 − $200,000 = $1,032,000

Its current annual profit is

Current profit = 40 weeks × 22,000 cans/week × $.70/can = $616,000

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

$1,032,000 − $616,000 = $416,000

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 business program believes that a survey of the university’s students can supply the needed information.

Accordingly, she organizes a survey that asks 500 students to keep track of the number of soft drinks they purchase on campus over the next 7 days.

Perform a statistical analysis to extract the needed information from the data. Estimate with 95% confidence the parameter that is at the core of the decision problem. Use the estimate to compute estimates of the annual profit. Assume that Coke and Pepsi drinkers would be willing to buy either product in the absence of their first choice.

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

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