# Question

The Aberdeen Development Corporation (ADC) is reconsidering the Aberdeen Resort Hotel project. It would be located on the picturesque banks of Grays Harbor and have its own championship-level golf course.

The cost to purchase the land would be $1 million, payable now. Construction costs would be approximately $2 million, payable at the end of the year 1. However, the construction costs are uncertain. These costs could be up to 20 percent higher or lower than the estimate of $2 million. Assume that the construction costs would follow a triangular distribution.

ADC is very uncertain about the annual operating profits (or losses) that would be generated once the hotel is constructed. Its best estimate for the annual operating profit that would be generated in years 2, 3, 4, and 5 is $700,000. Due to the great uncertainty, the estimate of the standard deviation of the annual operating profit in each year also is $700,00. Assume that the yearly profits are statistically independent and follow the normal distribution.

After year 5, ADC plans to sell the hotel. The selling price is likely to be somewhere between $4 and $8 million (assume a uniform distribution). ADC uses a 10 percent discount rate for calculating net present value. (For purposes of this calculation, assume that each year’s profits are received at year end.) Use ASPE to perform 1,000 trials of a simulation of this project on a spreadsheet.

(a) What is the mean net present value (NPV) of the project? (Hint: The NPV(rate, cash stream) function in Excel returns the NPV of a stream of cash flows assumed to start one year from now. For example, NPV(10%, C5:F5) returns the NPV at a 10 percent discount rate when C5 is a cash flow at the end of year 1, D5 at the end of year 2, E5 at the end of year 3, and F5 at the end of year 4.)

(b) What is the estimated probability that the project will yield an NPV greater than $2 million?

(c) ADC also is concerned about cash flow in years 2, 3, 4, and 5. Generate a forecast of the distribution of the minimum annual operating profit (undiscounted) earned in any of the four years. What is the mean value of the minimum annual operating profit over the four years?

(d) What is the probability that the annual operating profit will be at least $0 in all four years of operation?

The cost to purchase the land would be $1 million, payable now. Construction costs would be approximately $2 million, payable at the end of the year 1. However, the construction costs are uncertain. These costs could be up to 20 percent higher or lower than the estimate of $2 million. Assume that the construction costs would follow a triangular distribution.

ADC is very uncertain about the annual operating profits (or losses) that would be generated once the hotel is constructed. Its best estimate for the annual operating profit that would be generated in years 2, 3, 4, and 5 is $700,000. Due to the great uncertainty, the estimate of the standard deviation of the annual operating profit in each year also is $700,00. Assume that the yearly profits are statistically independent and follow the normal distribution.

After year 5, ADC plans to sell the hotel. The selling price is likely to be somewhere between $4 and $8 million (assume a uniform distribution). ADC uses a 10 percent discount rate for calculating net present value. (For purposes of this calculation, assume that each year’s profits are received at year end.) Use ASPE to perform 1,000 trials of a simulation of this project on a spreadsheet.

(a) What is the mean net present value (NPV) of the project? (Hint: The NPV(rate, cash stream) function in Excel returns the NPV of a stream of cash flows assumed to start one year from now. For example, NPV(10%, C5:F5) returns the NPV at a 10 percent discount rate when C5 is a cash flow at the end of year 1, D5 at the end of year 2, E5 at the end of year 3, and F5 at the end of year 4.)

(b) What is the estimated probability that the project will yield an NPV greater than $2 million?

(c) ADC also is concerned about cash flow in years 2, 3, 4, and 5. Generate a forecast of the distribution of the minimum annual operating profit (undiscounted) earned in any of the four years. What is the mean value of the minimum annual operating profit over the four years?

(d) What is the probability that the annual operating profit will be at least $0 in all four years of operation?

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