Investing in yet-to-be-opened toll roads is a risky business but, relative to the successes, the failures do seem to have something in common. They’re short slabs of tarmac.

Before a toll road is built specialist traffic forecasters attempt to estimate how much traffic will use the road. Their models are built around the time value of money – they assume that people attach a value to their time and will pay to save some of it.

Once you adjust for the inherent optimism required to win a bid, these models seem to work reasonably well for roads that cover long distances. Melbourne’s CityLink (22km), Sydney’s M2 (21km), M4 (40km) and M5 (32km) motorways and The Western Sydney Orbital (40km) have all been successful investments because the traffic projections have been close enough to accurate.

Toll roads don’t seem to work so well where the distances are short. Sydney’s Cross City Tunnel (2.1km) and the Lane Cove Tunnel (3.6km) are built on the same time value of money models but both have been abject failures – traffic has been less than half of what was forecast and equity investors won’t get a cent of their investment back.

It looks like people don’t value time after all. They value distance. Or perhaps they use distance as a proxy for time.

That would make some sense. The Cross City Tunnel might save 20 minutes of travel time but when you can see the other side of the city from the entrance, it doesn’t feel like it’s saving you much. Saving 20 minutes by careering along a 30km motorway at 110km an hour, on the other hand, feels well worth the money.

Distance is also much easier for us humans to quantify than time. The Cross City Tunnel might save 25 minutes one day and 15 the next but, in the absence of a daily stopwatch, it’s hard to know how much time you're really saving. You know for sure, on the other hand, that it is only 2.1km long.

The theory that time-value-of-money models don’t work for short distances is reinforced by the first-week data provided by listed company ConnectEast. It owns a 39-year concession on EastLink, a 39km pay-per-section road between Mitcham and Frankston in Melbourne’s south east. The road has just opened and the company reported an average of 134,000 cars per day in the first week of tolling – ‘only’ 30% less than the forecast average for the first month.

What’s interesting, however, is that the average toll and average trip length was 9% higher than forecast. People are using it as expected for the long trips but they’re not prepared to fork out for short distances, despite the same cost per minute of time saving.

With only one week of traffic data, it remains unclear whether enough cars will use ConnectEast’s 39km of road to justify the current security price, but it looks like there’ll at least be enough cash to cover the interest bill, which isn’t a bad start.

What, then, are the prospects for Brisbane’s 6km long RiverCity Motorway and the 6.7km BrisConnections Airport Link? If the ‘long trips only’ theory of toll road usage bears out, investors have plenty of reasons to be concerned.