You recently started working for OmiCon, a commercial real estate developer, and have been given a position working directly for Sophie Reynolds, OmiCon's CEO. When you meet Sophie for the first time, she gives you a project she wants you to complete by the end of the week.

Sophie explains that OmiCon is thinking about leasing a parcel of land to build a shopping center. OmiCon would own and operate the shopping center and generate revenue by renting space to retailers. Sophie would like you 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 OmiCon should be willing to pay to lease the land for the expected life of the project.

3. Determine if it is worth hiring a local consultant, Pete Berry, to do some additional market research that would provide a better estimate of the demand for retail space.

4. Write a short report summarizing the results of your analysis and any recommendations. Sophie tells you that Bob Bilkington, a former OmiCon employee, did some preliminary work on the project, but left the organization before wrapping things up. Sophie 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, Sophie 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 OmiCon 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 and a 50% chance that the true relationship would be where is the rental rate per square meter of floor space and 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 and 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 Sophie that doing this could lead to misleading conclusions about the real value of the project and how much OmiCon should be willing to pay to lease the land. Sophie 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, Pete Berry, who could do some additional market research to better identify which of the demand curves (i.e., or ) would actually be realized if the shopping center was built. Pete could do the study very quickly and would charge $50,000. To determine whether or not it was worth hiring Pete to do the additional research, Bob was going to evaluate two possible scenarios.

In the first scenario, he was going to assume that Pete would definitely identify the correct demand curve (e.g., if the real demand was, say, , Pete's report would state that the demand curve was ). And in the second scenario, he was going to assume that there was a 80% chance that Pete would identify the correct demand curve and a 20% chance that he would identify the wrong demand curve (e.g., if the real demand was, say, , there would be a 80% chance that Pete's report would correctly state that the demand curve would be and a 20% chance that Pete's report would mistakenly state that the demand would be ).

(HINT: In the first scenario, if OmiCon were to hire Pete, OmiCon will build a shopping center that is sized optimally for the demand curve that Pete identifies in his report. For example, if Pete's report says that the demand curve will be then OmiCon will build a shopping center that optimally sized for that demand curve. Similarly, if Pete's report says that the demand curve will be then OmiCon will build a shopping center that is optimally sized for that demand curve. Nonetheless, a decision to hire Pete does not affect the fact that there is still a 50% chance that the demand will actually turn out to be and a 50% chance that the demand curve will actually turn out to be .)

he identifies in his report. For example, if Pete's report says that the demand curve will be then OmiCon will build a shopping center that optimally sized for that demand curve. But in the second scenario, if Pete's report says the demand curve will be there is a 20% chance that demand curve will actually be . Similarly, if Pete's report says the demand curve will be there is a 20% chance that demand curve will actually be .)