Exercise 1: Sensitivity Analysis (45 points)

While preparing for winter season, a small town is considering applying a Road Salt policy for their streets, they estimate the initial investment needed for the policy in $20,000 (this amount already includes discounted operating costs for the period). The main impact of the policy is a decrease on traffic accidents (due to icy roads) and, given the size of the town, the city council is not interested in any other effect (such as decrease travel time) and won't consider them.

The council has gathered the following information (assume all stochastic variables are independently distributed):

Number of trips per month (during winter): between 30,000 and 50,000 with a mean at 40,000 (uniform distribution).

Accident probability per trip (during winter, with an icy road): between 0.01% and

0.05% with a mean at 0.03% (uniform distribution, also note, 0.01% = 0.0001),

Accident probability per trip (during winter, with a clear road): exactly 0.01%

Number of winter months: 3 months with a 50% probability, 4 months with a 50% probability.

Average cost per accident: $2,000 (already discounted to present day)

With all this information, the city council ask you to:

(a)(10 pts) Calculate the expected NPV of the base case (hint: since all variables are independently distributed, then we can use mean values).

(b)(10 pts) Create a partial sensitivity analysis graph for the NPV while varying the number of trips and the number of winter months throughout it's relevant values (hint, you can use more than one line/curve on the same graph).

(c)(10 pts) Create a partial sensitivity analysis graph for the expected NPV while varying the probability of having an accident per trip (during winter, with an icy road) throughout it's relevant values.

(d)(5 pts) Given the information available, what will be the best- and worst-case scenario for this policy compared to the status quo? (specify what values each variable will take).

(10 pts) Calculate the NPV for both the best and worst case scenario