Melon Enterprise is a commercial real estate developer. You recently joined Melon and your position reports directly to Pat Smith, the CEO. When you meet Pat for the first time, she asks you to work on a project that has to be completed in about a week.
Pat tells you that Melon is thinking about leasing a parcel of land to build a shopping center. Melon would own and operate the shopping center and generate revenue by renting space to retailers. Pat would like you to do some work on the project. Specifically, she would like you to complete the following tasks:
1. Determine the optimal size of the shopping center (to the nearest 100 square meters) based on existing estimates of the demand for retail space.
2. Determine the most Melon should be willing to pay to lease the land for the expected life of the project.
3. Calculate the profit under each possible demand curve with the optimum size of the shopping center.
4. Determine if it is worth hiring a local consultant, Roland Thomas, to do some additional market research that would provide a better estimate of the demand for retail space.
5. Write a short report summarizing the results of your analysis and any recommendations. Pat also informs you that Bob Devine, a former Melon employee, did some preliminary work on the project, but left the organization before wrapping things up. Pat says that you should have
complete confidence in any work Bob did on the project and that you should use his findings and assumptions as a starting point for your analysis. In fact, Pat has reviewed Bob’s notes and quickly summarizes the key information she thinks you’ll need for your analysis.
Specifically, she tells you that:
?Bob thought the shopping center would take one year to build and would last 20 years. He estimated that it would cost $100 per square meter to build and that the annual operations and maintenance costs would be $1 per square meter of floor space.
?Bob thought that the parcel of land would be large enough to build a shopping center with as much as 60,000 square meters of retail space. He also thought that Melon should make a one time upfront payment to lease the parcel of land for the expected 20-year life of the project.
?Bob thought the amount retailers in the shopping center would be willing to pay per square meter of floor space would be a decreasing function of the total size of the shopping center. Bob did some initial work estimating the likely relationship between what tenants would be willing to pay for retail space and the size of the shopping center. Specifically, he thought there was a 50% chance the true relationship would be:
r = 60 - 0.001s and a 50% chance that the true relationship would be r = 50 - 0.001s
where r is the rental rate per square meter of floor space and s is the total size of the shopping center in square meters. Furthermore, Bob was going to assume that once the shopping center had been built, the realized relationship between r and s would remain unchanged for
the next 20 years.
?Bob was planning to ignore discount rates and the time value of money in his initial evaluation of the project. He was going to treat all of the project’s costs and benefits equally no matter when they occurred in the life of the project; that is, he was going to treat a $1 cost incurred (or
revenue received) at the start of the project the same as a $1 cost incurred (or revenue received) during any other year of the project’s life. At this point, you tell Pat that doing this could lead to misleading conclusions about the real value of the project and how much Melon should be
willing to pay to lease the land. Pat agrees, but says she thinks this approach is good enough for a preliminary evaluation. (HINT: Do not try to account for the time value of money in your analysis. Simply treat all costs incurred [or revenues received] as equivalent no matter when they occur. Doing so means you can calculate the total costs over the life of the project by simply summing the costs incurred in each year. Similarly, you can calculate the total revenues received over the life of the project by simply summing the revenues received in each year.)
?Bob had contacted a local consultant, Roland Thomas, who could do some additional market research to accurately forecast which of the demand curves (i.e., r = 60 - 0.001s or r = 50 - 0.001s) would actually be realized if the shopping center was built. Bob was trying to find out if it was worth hiring Roland at all, and if he could be hired then what was the maximum consulting fee that Melon should offer.
(HINT: In the first scenario, if Melon were to hire Roland, Melon would build a shopping center that is sized optimally for the demand curve that Roland identifies in his report. For example, if Roland’s report says that the demand curve will be r = 60 - 0.001s then Melon will build a shopping center that is optimally sized for that demand curve. Similarly, if Roland’s report says that the demand curve will be r = 50 - 0.001s, then Melon will build a shopping center that is optimally sized for that demand curve. Nonetheless, a decision to hire Roland does not affect the fact that there is still a 50% chance that the demand will actually turn out to be r = 60 - 0.001s and a 50% chance that the demand curve will actually turn out to be r = 50 - 0.001s)