Last week I published a post outlining ways to start evaluating the benefits of rail extensions in terms of costs and benefits. I used projected ridership, projected cost and a discount rate (because future benefits aren’t as valuable as present benefits) to derive an approximate subsidy per ride for a given rail extension. I emphasize approximate in part because a single number derived from a single ridership estimate for a single year can only provide so much information. But I also say approximate because I wasn’t as precise as I could have been with the costs and benefits. With Sound Transit proposing its draft Sound Transit 3 ballot measure, a decided to do a more detailed analysis of the costs and benefits of the proposal.

The basics of the analysis are the same. I still use Sound Transit’s ridership numbers and project costs and continue to use annuities to assess benefits over time. I increased my discount rate to 3% and assumed that the capital benefits last in perpetuity from the date the service is expected to open (these changes mostly cancel each other out). I also included annual operational costs into the analysis and I assumed that taxpayers pay taxes to cover project costs annually. Finally, I looked at scenarios where ridership was constant and where ridership increased by 0.5% per year. All ridership estimates use Sound Transit’s numbers, which estimate ridership in 2040.

For projects, I looked at all the rail projects (including infill stations) for which reliable ridership estimates existed, plus the two large BRT projects that are proposed as part of the ST3 draft proposal. This should cover well over 95% of proposed spending.

Before diving into the data, it’s worth defining what “subsidy per ride” means because it is the basis for analyzing the benefits of the investment. Subsidy per ride is the amount of social value we place on the average ride on the transit service. Since transit (or at least this transit) doesn’t pay for itself at the fare gates, we need to have some value for the amount that we are willing to subsidize a ride. This value comes from positive externalities such as emissions reductions and congestion alternatives. Coming up with an exact value is difficult, but farebox recovery rates for bus service provide a good litmus test.

Theoretically, bus subsidies should on average be higher than rail subsidies because buses also provide lifeline service, a social equity concern that rail systems don’t address. King County Metro has a 29% farebox recovery rate and fares ranging from $2.50 to $3.00. Sound Transit has a 22% farebox recovery rate and fares ranging from $2.25 to $5.75 for Sounder commuter rail. Given these numbers rail investments should probably have at least a 30% farebox recovery rate per dollar of subsidy though the case can be made for higher or lower subsidies.

In the tables below an $8.33 subsidy per ride corresponds to a 30% farebox recovery rate with $2.50 fare. Similarly, a $10 subsidy per ride corresponds to a 25% farebox recovery rate and a $7.00 subsidy per ride corresponds to a 35.7% farebox recovery rate. Unfortunately, Sound Transit does not provide more detailed fare information.

Here is the data on the net benefits and return on investment for each subarea and the region as a whole with dollar values in millions of dollars. **Edit: Detailed formulas posted at the end of the post.** For those not familiar with subarea system, the Sound Transit district is divided into five subareas and every dollar raised in a given subarea must also be spent in that subarea.

Net benefits (in millions of dollars) with 0.5% annual ridership growth.

Return on investment (1 = break even) with constant annual ridership.

Net benefits (in millions of dollars) with constant annual ridership.

Return on investment (1 = break even) with constant annual ridership.

The data tells a fairly sad story.

The most basic problem is that under less generous assumptions, the net value of the package is actually negative. That’s really troubling given that capital investments of this sort should have at least a 15% return on investment given the deadweight losses associated with taxes. And return on investment should probably be five to ten percentage points higher given that Sound Transit 3’s revenue will come from nasty regressive sales taxes. Only three out of the six scenarios meet the 15% threshold.

But the more harrowing issue is the hugely inefficient use of resources. Three of the five subareas (South King, East King and Snohomish) have a negative return on investment even with the most generous assumptions. There are lots of big projects here whose benefits do not come remotely close to covering their costs. Of course, some amount of pork to grease the wheels for a vote is inherent to the political process. But the amount of extremely wasteful spending in this proposal is rather shocking and far higher than Sound Transit 2. Notice all the red in the tables below, which show the data project by project. The net benefits for many projects are negative (and usually extremely negative) even under the most generous $10 subsidy per rider assumptions.

If there is a silver lining to this analysis it is as a reminder for why rail investment in Seattle proper is so important. Even under more conservative assumptions, North King projects create over $2.7 billion dollars of value for the region and a 57% return on investment.

Overall, given these numbers and the amount wasteful spending in this project, I don’t see myself voting for it as it stands. Fortunately, the plan is not final and you can still give feedback to Sound Transit.

***EDIT: the actual specific formulas for calculating costs and benefits are:**

**Y = Projected Opening Year – Current Year**

**Benefit with .5% ridership growth**

**Benefit = (Subsidy * (Ridership / (1.005 ^ Y)) * 365 – Operational Costs) * (1/.025 – (1 – (1.005/.03) ^ Y) / .025)**

**Benefit with constant ridership**

**Benefit = (Subsidy * Ridership * 365 – Operational Costs) * (1/.03 – (1 – (1/.03) ^ Y) / .025)**

**Costs:**

**Cost = Annual Paymnet * (1– 1.03^–25)/0.03 where**

**Sticker Price = Annual Payment * (1 – (1/.99) ^ 25) / -.01 (assumes tax base grows by 1% a year).**

**Assuming population increases by 1% per year reduces total cost by about 1.5% over 0 population growth.**