The Think-Big Development Co. is a major investor in commercial real estate development projects. It currently has the opportunity to share in three large construction projects:

Project 1: A high-rise office building

Project 2: A hotel.

Project 3: A shopping center.

Each project requires making investments at four different points in time: a down payment now and an additional capital after one, two and three years. Table 1 shows the total amount of investment capital required from all of the partners at these four points in time for each project. Thus, a partner taking a certain percentage share of a project is obligated to invest that percentage of each of the amounts shown in the table for the project.

All three projects are expected to be very profitable in the long run. So the management of Think-Big wants to invest as much as possible in some or all of them. Management is willing to commit all of the company’s capital currently available, as well as additional investment capital expected to become available over the next three years. The objective is to determine the investment mix that will be most profitable, based on current estimates of profitability.

Since it will be several years before each project begins to generate income, which will continue for many years thereafter, we need to take into account the time value of money in evaluating how profitable it might be. This is done by discounting future cash outflow (capital invested) an cash inflows (income), and then adding discounted net cash flows to calculate a project’s net present value.

Based on current estimates of future cash flows (not included here except for outflows), the estimated net present value for each project is shown in the bottom row of Table 1. All the investors, including Think-Big, then will split this net present value in proportion to their share of total investment.

For each project, 100 one(1) percent shares (or fraction thereof) are being sold to major investors, such as Think-Big, who become partners for the project by investing their proportional shares at the four specified points in time. For example, if Think-Big takes 10 shares of the project, it will need to provide $4 million now, and then $6 million, $9 million, and $ 5 million in year 1, 2 years, and 3 years respectively.

The company currently has $25 million available for down payment, $20 million after one year, $20 million more after two years, and another $15 million after three years. Assume that money left over at the end of the year can be used the following year (no interest accrues though). How many shares should Think-Big take in the respective projects to maximize the total net present value of these investments? (Use Linear Programming to find the optimal investment strategy).

Financial data for the projects being considered for partial investment by the Think Big Development Co.

Investments Capital Requirements

Year High-Rise Hotel Shopping Center

0 $40 million $80 million $90 million

1 $60 million $80 million $60 million

2 $90 million $80 million $20 million

3 $50 million $70 million $40 million

Net Present Value $45 million $70 million $50 million

Use the optimal solution of the Linear Program (i.e. optimal number of shares invested in each of the three decisions; the high-rise building project, the hotel project and the shopping center project) to solve the following Risk Analysis problem.

The partners in the project, including Think Big Co., would spend three years with the construction, then retain ownership for three years while establishing the property, and then sell the property in the seventh year.

However Think-Big management understands very well that such decision should not be made without taking risk into account. These are very risky projects since it is unclear how well these properties will compete in the marketplace when they go into operation in a few years. Although the construction costs during the first three years can be estimated fairly closely, the net income during the following three years of operation are very uncertain. Consequently, there is an extremely wide range of possible values for each sale price in year 7. Therefore management wants risk analysis to be performed in the usual way (with computer simulation) to obtain risk profile of what the total NPV might actually turn out to be with this proposal.

To perform this risk analysis, Think-Big staff now has devoted considerable time to estimating the amount of uncertainty in the cash flows for each project over the next seven years. These data are summarized in the following table. (In units of hundred thousands of dollars per share taken in each project). In years 1 through 6 fro each project, the probability distribution of cash flow is assumed to be a normal distribution, where the first number shown is the estimated mean and the second number is the estimated standard deviation of the distribution. In year 7, the income from the sale of the property is assumed to have a uniform distribution over the range from the first number shown to the second number shown.

Use Crystal ball to simulate the NPV for 10,000 trials, assume a cost of capital of 10 percent per year.

Calculate a 98% confidence interval for NPV.

Think Big’s estimated cash flows per share taken in the Hotel and Shopping Center Projects.

Hotel Shopping Center Project

Year Cash flow ($100,000) Year Cash Flow ($100,000)

0 -800 0 -900

1 Normal(-800,50) 1 Normal(-600,50)

2 Normal(-800,100) 2 Normal(-200,50)

3 Normal(-700,150) 3 Normal(-400,100)

4 Normal(300,200) 4 Normal(250,150)

5 Normal(400,200) 5 Normal(350,150)

6 Normal(500,200) 6 Normal(400,150)

7 Uniform(2000,8440) 7 Uniform(1600,6000)