year	2020	2025
newspaper	20	50	25	16	25	30	25	22	29	15	30	20
pair of jeans	60	75.99	75	55	50	65	55	50	34	55	70	30
1- bedroom apartment	700	988	920	950	975	930	800	850	1100	1050	900	800

For the each item, use their YEAR 2025 results to determine

(1) Use the mean YEAR2025 prices are the base price. Consider the total cost (total cost = 100 newspaper+3 jeans+1 apartment) is the NPV of project. Draw the sensitivity diagram for the three major variables. Include important calculations and discussion on the results.

(2) If the NPV = 3(jeans) 2 + (apartment)(newspaper), redo the questions in (1).

(3) Use the established distribution histogram (function) to draw sensitivity diagram with 30% and 70% probability contours. Include important calculations and discussion on the results.

Q2)

A developer is planning an outlet shopping center. At the project appraisal stage, two contract methods are under consideration: 1. Design-building (DB) approach, 2. Design-bidbuild (DBB) approach. Predicted 12 year cash flows for the construction phase and operation phase of this project is listed in Table 1 for those two optional contract methods. For DB approach, the construction will only take 2 years but cost more. For the DBD approach, the construction will take 3 year but cost less. The developer is evaluating the performance of the project in a 12 year window by using the NPV.

Table 1: Cash flow (unit $M)

year	1	2	3	4	5	6	7	8	9	10	11	12
DB	-3	-5	0	1	1	1	1.2	1.2	1.3	1.3	1.3	1.5
DBB	-1	-3.5	-3	0	1	1	1.2	1.2	1.3	1.3	1.3	1.5

(1) Calculate the NPV for those two contract methods, and identify the construction method of choice for the developer. (Assume rate of return is 5%)

(2) The increase in construction cost (cash flow) and the decrease in profit in the operation phase can be two risks that the developer shall consider. Plot sensitive analysis results for those two risks cost for the construction method of choice in problem (1). Show detail calculations. (Hint: for the sensitive plot, the y-axis should be the % change in NPV, x-axis should be % change in risks. You can assume the changing percentage in cash flow is same for each year during the construction and the operation phases. The sensitive curves for the two risks may not be linear, therefore you need to plot multiple points, then connect them to form the curve)

(3) Assume the construction cost increase follows a triangle probability distribution (0, 5%, 10%), and the profit decrease follows a uniform probability distribution (-5%, 5%), as shown below. Draw the sensitive curves with 25% probability contour.