Moody’s has come out with its rating of $500 million worth of senior revenue bonds for the $1.06 billion arena portion of the $4.9 billion Atlantic Yards project in Brooklyn.

The rating for the arena, called the Barclays Center, is Baa3, the lowest investment-grade rating available.

And Atlantic Yards largely got the rating on the strength of New York City taxpayers taking a big risk.

The mechanics of the financing aren’t that difficult. A subsidiary of Albany’s Empire State Development Corporation, the Brooklyn Arena Local Development Corporation (BALDC), will own the arena.

ArenaCo, a company owned in turn by developer Bruce Ratner and his partner, Russian billionaire Mikhail Prohkorov, will make payments in lieu of taxes (PILOTs) to BALDC in return for the long-term right to use the arena.

In turn, BALDC will turn those PILOTs over to the PILOT trustee, which will then use the funds to pay off the debt.

The PILOTS, and thus the bonds, depend on revenues from the arena for payment: “premium seating licenses and sales, sponsorship agreements, … concession revenues,” and the like, note Moody’s.

While ArenaCo does have a contractual obligation to pay debt service, it is a special-purpose company without recourse to any if its owners’ other companies or assets. Mikhail Prohkorov, Ratner’s equity partner, has agreed to keep the Nets themselves solvent, for example, but not to keep the arena solvent, according to Bond Buyer.

The security of the bonds, then, does not really depend on Ratner or Prohkorov. Indeed, the rating document says that the trustee can “foreclose on the Arena in the event of non-payment of PILOTs,” with the current owners “dispossessed of the Arena.”

So how did we arrive at the investment-grade rating, without recourse to deep pockets?

Rating a bond isn’t a static process. A project’s sponsors don’t bring their structure to the raters and ask for a grade. Instead, they negotiate on how to structure the deal to get to achieve certain goals that each rating class requires.

The math is simple: bond investors want to see project cash flows “cover” annual debt payments a certain number of times. The higher this “coverage ratio,” the higher the rating.

This is because a higher coverage ratio allows for plenty of room for error  — and for bondholders to be repaid — if cash-flow estimates turn out to be wrong.

On projects that don’t seem very risky — like a power plant with strong industrial customers that have agreed to pay a certain amount for power for the life of the bonds — raters and investors don’t require a big coverage-ratio number, because the risk that the revenue will fluctuate seems low.

For some “safe” projects, the coverage ratio can be well below two, because nobody thinks that revenues will fluctuate very much.

On the Barclays Center, though, the debt service coverage ratio is a hefty 2.85 times. This means that raters and potential investors likely aren’t that confident that revenues will materialize exactly as expected.

Indeed, Moody’s notes that if we look at revenue that is already contracted for, the debt service coverage ratio is only .95 times in the first year (less than 1).

So the raters built in lots of room for error, and, even beyond that, required a cash reserve fund up front that’s enough to cover a year’s worth of debt payments.

How do you get a high coverage ratio? You can’t make up revenue, so, you’ve got to keep debt down.

On these senior bonds, Atlantic Yards is keeping debt way down. Raters have required a 40 percent equity component for this part of the deal.

This is important: It’s likely only because of this huge equity component that Atlantic Yards could attain even this low investment-grade rating.

As on any debt-financing project, equity holders are on the hook for the first losses if the arena can’t pay its debt and faces foreclosure.

So who are the equity holders on the hook for this risk?

Ratner and Prohkorov share $293.4 million of such exposure, as they should.

But New York City has $131 million in such equity exposure — nearly as much as Ratner and Prohkorov each.

This means, in effect, that if Atlantic Yards can’t pay its debt, New York City taxpayers stand to lose a substantial investment along with Ratner and Prohkorov.

So in the event of a shortfall, New York City will be tempted to effect a bailout of the debt portion so as not to lose its taxpayers’ equity investment. The raters at Moody’s astutely note that this “$131 million commitment from New York City demonstrates strong municipal government support for this project.”

Despite other analysis of things like the strength of New York’s media market, etc., this part of the transaction is likely all that potential bondholders care about.

They can see that there is a huge cushion of equity that will absorb losses before bondholders will — and that the cushion itself has plenty of extra padding because of New York City taxpayers’ position.

In fact, it is interesting to wonder whether the arena could have attained this investment-grade rating if it were only Ratner and Prohkorov putting up the equity.

Beyond this $500 million senior bond issuance, another $146 million in lower-rated bonds are forthcoming …