Kevin Downing, a reader in Portland, got me hooked on a fascinating exercise: trying to figure out how long it takes a road expansion to pay for itself. Let’s take a look at how this might work. (But please stick around for all the caveats at the end.)

Consider, for example, the Delta Park Project in north Portland. It’s a \$60 million endeavor that will add one lane in each direction to a 1.2 mile-long segment of Interstate 5, which currently has two lanes in each direction. So the question is: will road-users on that segment pay for the \$60 million price tag?

Here’s how I see the numbers. Assuming fuel efficiency of 22.5 miles per gallon, on average, a typical passenger vehicle would burn a bit more than 0.05 gallons of gasoline to drive that 1.2 miles of roadway. Multiply the fuel usage by the federal gasoline tax of 18.4 cents per gallon, as well as by the Oregon gasoline tax of 27 cents per gallon (a figure that includes the 3 cent per gallon add-on for Multnomah County), and you find that a single trip on that section of road yields a little less than 2.5 cents in revenue.

So far so good. Now let’s assume that the average daily traffic volume is 124,833 vehicles. (That’s the average of the official numbers I got from ODoT from four monitoring points.) If each of those vehicles generates the average revenue, then a day’s worth of travel nets \$3,015. That’s not much. In fact, in order to pay for the \$60 million investment, you would need nearly 20,000 days of travel revenue. Put in simpler terms, it would take road-users more than 54 years to pay for the road expansion.

And it’s probably much worse, because my simplistic accounting leaves out a lot.

• For one thing, I’m assuming that the revenue from fuel burned on all six lanes of the expanded freeway is used to pay off the cost of the two new lanes. If the two new lanes had to pay for themselves, then the payback period could be more like 150 years.

I’m also not factoring in any financing costs. Nor am I accounting for overhead related to administration, contract management, or other government costs that aren’t directly included in the Delta Park Project budget. (And I’m not discounting future tax receipts or doing anything fancy like that.) If the real price tag is greater than \$60 million, then we’re looking at a longer payback period.

Plus, I’m assuming that vehicle fuel efficiency stays unchanged for the next 54 years. If cars get more efficient, then each trip will generate less revenue, and therefore require a longer time period to pay for the road expansion.

On the other hand, I should be fair: the tax rate could go up faster than fuel economy improves (or some other tax, like the mileage tax, could kick in) and revenues from driving could come in faster than I’ve calculated, making for a shorter payback period. Well, maybe.

I’ve also assumed that the traffic volume remains unchanged over the next 54 years, but it may not. If driving gets more expensive—whether because of new taxes or rising world oil prices—then it’s likely that people will drive fewer miles. And a lower traffic volume on that road segment would, once again, make for an even longer payback period.

Of course to be fair, the traffic volume on that section of I-5 could increase. Road widening often encourages more driving, which would mean more revenue, and therefore a shorter payback period. Interestingly, however, the Department of Transportation does not believe there will be any increase in traffic volume because of the new lanes.

Then there’s all the other stuff I didn’t factor in. When I say that the road pays for itself in 54 years, I’m not counting the direct costs that a road incurs such as cleaning, maintaining, resurfacing, and repairing it. Nor I am counting the cost of lighting it, policing it, and so on. What’s more, I’m not counting the costs of any of the “externalities” of road use, including the carbon emissions that contribute to climate change, the air pollution that harms human health, the water pollution that degrades rivers and lakes, or the noise that reduces quality of life and property values alike; nor am I counting the economic costs of property damage, injuries, and fatalities that arise from collisions on the road segment.

That said, the road widening may help reduce the cost of some current externalities, such as time lost to traffic congestion. It’s difficult to make such a calculation. And it’s made harder by the fact that the construction itself usually causes further congestion, and even the congestion benefits of new lanes tend to be short-lived.

Whew!

What else didn’t I calculate? Trucks for one. Trucks in Oregon are subject to a weight-mile tax that, in theory, is designed so that truckers pay the cost of their disproportionate impact on roads. For the purposes of my chicken-scratch calculation here, I’ve simply assumed that trucks actually do pay for themselves, which may not be a safe assumption.

Leaving trucks out does pose a few analytical hazards though. They put a lot of strain on road surfaces, and they tend to increase congestion and boost the cost of other externalities like air pollution and noise. But because they also burn more fuel than cars, they also generate more revenue from fuel taxes.

Is anyone still reading? Anyone?

So, okay, the bottom line is this: road expansions don’t pay for themselves.

It’s certainly true that getting an accurate accounting requires more workmanship than I’ve put into this blog post, but the balance of factors seems to pretty clearly suggest that the payback period is very long.

You might quibble that the Delta Park Project isn’t a good example; that other projects are less expensive. And I’ll concede that this freeway example includes bridge and ramp reconstruction. Yet it’s also true that there are no right-of-way or displacement costs, and the four existing lanes are functioning okay already. So a new road project is likely to be even more expensive than this one.

What about the really big-ticket project next door, the Columbia River Crossing? Well, someone else will have to do that calculation.

And Seattle’s deep-bore tunnel? (No, I can’t help myself. It’s a sickness.)

It will pay for itself in a mere 14,506 years. (That’s using figures for the “no-toll” scenario.) Just think: if we had built it during the late Upper Paleolithic period, it would have almost paid its own way by now.

Photo depicts the Delta Park area; from the Oregon Department of Transportation.