## Sunday, 20 November 2022

### Transport Maths

Transport projects run their own version of benefit-cost accounting. It's weird to the sector, but apparently common internationally.

Normally you'd want to go ahead with a project if it provides net benefits, where benefits are counted comprehensively and costs are counted comprehensively. If a project provides net benefits, it'll also have a benefit-to-cost ratio that's greater than 1.

I never much worried about it whether they were using BCRs or net benefits.

They're instead something a lot more like a "net benefit per dollar of transport expenditure" measure. Costs that aren't financial costs to NZTA wind up as disbenefits that are netted from benefits in the numerator of their ratio.

And that difference can matter.

Imagine two projects, each of which would result in one statistical life-saving valued at \$5m. That’s on the benefit side. Neither project has any other benefits.

Project A would impose \$4m in costs on drivers through reduced speed limits (increased travel time) and a \$100,000 financial cost to NZTA in changing speed limit signs. So it has net benefits of \$5m - \$4m - \$0.1m = \$900k.

Its true benefit-cost ratio, where all benefits are counted on the benefit side and all costs are counted on the cost side, is 1.2:1. NZTA’s 'net benefit per dollar spent' measure would have it as 10:1.

Project B would spend \$1m on median barriers and impose \$100,000 through visual disamenity costs and hassles while the barriers are being installed. It has net benefits of \$5m - \$1m - \$0.1m = \$3.9m. The true benefit-to-cost ratio, where all costs are weighed against all benefits, is 4.5:1. NZTA’s 'net benefit per dollar spent' measure would have it as 4.9:1.

In this example, project B has much higher net benefits, and a much higher true BCR.

But a transport ranking would prefer project A.

It's a made-up example with made-up numbers, but I wonder how many real-world cases wind up with this problem.

If NZTA were mainly weighing up projects that had comparable bundles of financial and 'disbenefit' costs it probably wouldn't much affect things. But where more of the options, like blanket reductions in road speeds, mainly have costs that get netted from numerators while having trivial financial cost to NZTA, it could be a problem.

It might be worth NZTA checking whether their method remains fit for purpose or whether it's likely to cause issues. Alternatively, it would be a fun student project.