Question

Some Rough Cost-Benefit Numbers for a “Bridge to Nowhere”

A widely publicized federal earmark in the 2006 transportation appropriation bill was $223 million for a bridge intended to provide access to Ketchikan, Alaska’s airport on lightly populated Gravina Island. The project had the misfortune to become labeled the “Bridge to Nowhere” when the earmark came to light in the 2008 presidential campaign. It is possible to do some rough cost-benefit analysis on the project.

Gravina Island has a population of around 50, so most of the bridge traffic would likely be those using the airport. The island was not inaccessible without the bridge. A ferry serves the island, with ferries leaving every half hour. The primary impact from the bridge would be to reduce travel time on the trips. It has been estimated that the drive to the airport from Ketchikan would take 13 minutes, compared to 27 minutes by ferry. Therefore, the time saving is around 15 minutes per passenger. Ketchikan is a port for cruise ships, which dock on the mainland, so some of the bridge traffic would be ship passengers either joining or leaving the cruise ships. Airline enplanements/deplanements (total passengers coming and going through the airport) are on the order of 400,000, so that traffic would create 800,000 crossings of the bridge. But let’s be generous and round up to 1,000,000 crossings, each saving around one quarter hour by taking the bridge.

How much is the time saving worth? Let’s assume that each visitor earns $125,000 in income per year. If the visitor works 50 weeks per year and 40 hours per week, then the work year is 2,000 work hours. Some visitors are children and some are retired—and the earning level assumed here is much higher than the national average—but let’s not worry about that. Work it out with different estimates on your own, if you wish. With these numbers, the value of work time equals $62.50 per hour. But this is leisure time for most of the traffic, not work time, so let’s adjust the value downward by 50 percent (probably an underadjustment) to get an estimate of the value of leisure time—$31.25. Each passenger saves 15 minutes with the bridge (compared with travel by ferry), so the saving per passenger equals $7.81. Multiply that by 1 million passengers to get $7,810,000.

We will assume that the bridge will last forever and will have no maintenance cost and that 3 percent is a reasonable discount rate (that’s lower than the OMB rate of 7 percent, but probably higher than current market interest rates). Divide $7,810,000 by 0.03 (because benefits are perpetual—the value is lower if we use a finite life for the bridge) to get the present value of the services from the bridge of $260.4 million, a large number and, as it turns out, larger than the amount of the appropriation. (If you are uncomfortable with perpetual life, use 100 years and the annuity formula to get a present value of services: (7.81/0.03)[1 − (1/1.03)100] 5 $246.8 million.)

But that is not the end of the story. In order to make the bridge functional, the state of Alaska has to spend $165 million in addition to the federal government’s $233 million. Summing up, the present value of the benefits of the bridge is at most $260.4 million, but its total cost is $398 million.

1. Would you consider the bridge to be a worthwhile use of federal resources? Why or why not?

2. Why might the state of Alaska be interested in getting the bridge built, even though the total cost of the bridge exceeds the present value of the benefits from the bridge? From the standpoint of Alaska, what are the relevant costs and benefits?

3. How do the benefit-cost analysis results change if the discount rate is 7 percent? What about 2 percent?

Answer 1

1. Let us examine out data points

Total crossing in the bridge =1,000,000

Time saved = 15 minutes

Cost of work =$62.50 per hour

Value of leisure =$31.25

Savings per passenger =$7.81

Total Saving = $7.81*1,000,000=$7,810,000

Discount rate = 3%

Present value of services =$7,810,000/0.03 =$260.4 million

Total expenditure on the construction of bridge=($165+$233)million =$398million

total loss= $398 million - $260.4 million = $137.6 million

Thus is it very evident that cost of construction of bridge outweighs the benefits received from the bridge so construction of the bridge is not worthwhile.

2. The state of Alaska might be justified in building the bridge as the cut in the time of travel might encourage outsiders to come into the region and increasing its sparse population. The time saved could be crucial in times of medical emergencies as a cost of living cannot be evaluated in economic terms.

3. Discount = 7%

Present value of services =$7,810,000/0.07 =$111.5 million

Total loss =$398 million - $111.5million = $286.5 million

Discount =2%

Present value of services =$7,810,000/0.02 =$390.5 million

=$398 -$390.5

=$ 7.5 million

Please leave a feedback if you like the answer. It will provide us encouragement to even get better and the encouragement means a lot. Thanks for your question. It was a pleasure working on drafting the answer to this very involved question.