Fundamentals of Transportation/Evaluation/Solution2

 Solution:

Benefits considered are only Travel Time Savings.

Travel Time Savings = 2,000 Commuters x 0.5 Hours/day (30 minutes/day)

Travel Time Savings = 1000 Commuters-Hours/day x 5 days/week 52 weeks/year

Travel Time Savings = 260,000 Commuters-Hours/year

Travel Time Savings start after two years (given in the problem statement). Other assumptions are: Present Year is 0, no growth (constant commuters ev- ery year, and thus constant savings), and constant Value of Travel Time (VOT). Therefore, Benefits must be discounted to Present value for each year and added for a total during the lifespan of the project considered (30 years).

Adding up all Present Value of Travel Time

Present Value of Travel Time = (VOT )(260,000)(1/[1+0.03]^2 + 1/[1+0.03]^3 + ... + 1/[1+0.03]^29 + 1/[1+0.03]^30)

You can sum it up in an excel spreadsheet or recognize that this is a geometric series.

The sum is 18.63 inside the parentheses.

Total Present Value of Travel Time = (4,843,687.57)(VOT)

Costs are given by Total Present Value of $320,000,000.

Benefits/Costs = 1

Thus

(4,843,687.57)(VOT)/320,000,000 = 1

VOT = USD$66/Hr.

The VOT must be at least 66 US dollars.

/Solutions