CASE FOR DISCUSSION

CASE $71$

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 air$-$ port 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 $2008$ presi$-$ dential campaign. It is possible to do some rough cost$-$benefit analysis on the project.Gravina Island has a population of around fifty, 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 thirteen minutes, compared to twenty$-$seven minutes by ferry. Therefore, the time saving is around fifteen 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 join$-$ ing 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 $$125,000$ in income per year. If the visitor works fifty weeks per year and forty hours per week, then the work year is $2,000$ work hours. Some visitors are children and some are retired$$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 esti$-$ mates on your own, if you wish. With these numbers, the value of work time equals $$62\mathrm{.}50$ per hour. But this is leisure time for most of the traffic, not work time, so let$$s adjust the value downward by $50$ percent $($probably an underadjustment$)$ to get an estimate of the value of leisure time: $$31\mathrm{.}25.$ Each passenger saves fifteen minutes with the bridge $($compared with travel by ferry$),$ so the saving per passenger equals $$7\mathrm{.}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 $0\mathrm{.}03($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\mathrm{.}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: $(7\mathrm{.}81/0\mathrm{.}03)[1(1/1\mathrm{.}03)100]5$ $$246\mathrm{.}8$ million.$)$ But that is not the end of the story. To make the bridge functional, the state of Alaska has to spend $$165$ million in addition to the federal government$$s $$233$ mil$-$ lion. Summing up$,$ the present value of the benefits of the bridge is at most $$260\mathrm{.}4$ million, but its total cost is $$398$ million.

Consider These Questions $($Read case $7-1$ on pp$\mathrm{.}352-353$ in chapter $7$ in Mikesell $($Some Rough Cost$-$Benefit Numbers for a $$ Bridge to Nowhere$)$ and answer the questions on p$\mathrm{.}353.$ When you work on this problem, remember, cost$-$ benefit analysis is all about numbers. The answers to questions $1-3$ should be numerical:$)$

$1-$ Would you consider the bridge to be a worthwhile use of federal resources?

$2-$ 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?