Problem 1 (50 points)
The city of San Diego is considering extending the trolley (the downtown mass transit train) 11 miles from Old Town up to La Jolla. The cost of construction would be $1.7 billion. The
estimated ridership along the new section is 18 thousand per day work day (use only the
weekday commuters for your calculations), and the daily cost of operation and maintenance is $60,000 (the trolley operates every day of the year). Assume that the opportunity cost of
financial capital is constant at 7%. The average time saved by commuters if using the trolley instead of driving during rush hour will be a half hour (30 minutes) each way, and they will save 3 gallons of fuel per day. The price of fuel is $3.50 per gallon. The average salary of commuters if $37,000 per year. To convert things to per-hour numbers, use 52 weeks per year and assume 40-hour work weeks.
a) Should the trolley extension be undertaken? Show your calculations.
b) What if you factor in that cars emit carbon dioxide? Scientists have estimated that
every metric ton of carbon dioxide leads to climate change that will generate a social
cost of $12. Does this change your answer in (a)? Use the fact that there are 20 pounds of CO2 per gallon of gas, and that there are 2,204 pounds to a metric ton. Again, show your calculations.
To determine if the trolley extension should be undertaken, we need to calculate the net present value (NPV) of the project. The NPV takes into account the initial cost of construction, the operating and maintenance costs, the time and fuel savings for commuters, and the opportunity cost of financial capital.
a) Calculating the NPV:
Step 1: Calculate the yearly savings for commuters:
- Time savings: Each commuter saves 30 minutes (0.5 hours) each way, making it 1 hour per day. There are 18,000 weekday commuters, so the total time saved per year is 18,000 * 1 hour * 250 work days = 4,500,000 hours.
- Fuel savings: Each commuter saves 3 gallons of fuel per day, which is 18,000 * 3 gallons * 250 work days = 13,500,000 gallons per year.
Step 2: Calculate the yearly cost savings for commuters:
- Time savings: Using the average salary of $37,000 per year, and assuming 40-hour work weeks and 52 weeks per year, the hourly wage is $37,000 / (40 hours/week * 52 weeks/year) = $17.79 per hour. The time savings of 4,500,000 hours gives a yearly cost savings of 4,500,000 hours * $17.79/hour = $80,055,000.
- Fuel savings: The fuel savings of 13,500,000 gallons multiplied by the price of fuel at $3.50 per gallon gives a yearly cost savings of 13,500,000 gallons * $3.50/gallon = $47,250,000.
Step 3: Calculate the yearly net cash flow (cost savings - operation and maintenance costs):
- Yearly net cash flow = $80,055,000 + $47,250,000 - $60,000 = $127,245,000.
Step 4: Calculate the NPV using the opportunity cost of financial capital at 7%:
- The NPV formula is: NPV = (Year 1 net cash flow) / (1 + discount rate)^1 + (Year 2 net cash flow) / (1 + discount rate)^2 + ... + (Year n net cash flow) / (1 + discount rate)^n.
- In this case, since the trolley operates every day of the year, we can assume that the yearly net cash flow remains constant over the project's lifetime.
- Therefore, NPV = $127,245,000 / (1 + 0.07)^1 + $127,245,000 / (1 + 0.07)^2 + ... + $127,245,000 / (1 + 0.07)^n.
b) Taking into account the social cost of carbon dioxide emissions:
Step 1: Calculate the yearly CO2 emissions by car commuters:
- Each gallon of gas emits 20 pounds of CO2, which is 13,500,000 gallons * 20 pounds/gallon = 270,000,000 pounds of CO2 per year.
- Convert this to metric tons by dividing by 2,204 pounds/metric ton: 270,000,000 pounds / 2,204 pounds/metric ton = 122,488 metric tons of CO2 per year.
Step 2: Calculate the yearly social cost of carbon dioxide emissions:
- Each metric ton of CO2 leads to a social cost of $12, so the yearly social cost is 122,488 metric tons * $12/metric ton = $1,469,856.
Step 3: Include the social cost in the NPV calculation:
- For year 1, the net cash flow is $127,245,000 - $1,469,856 = $125,775,144.
- NPV = $125,775,144 / (1 + 0.07)^1 + $127,245,000 / (1 + 0.07)^2 + ... + $127,245,000 / (1 + 0.07)^n.
Compare the results in part a) and part b) to determine if the inclusion of the social cost changes the decision to undertake the trolley extension.