In proposing to renew the Build America Bonds program, the Obama administration last week set an audacious goal: more benefit at the same cost.

As explained in numerous papers and reports the past few years, the federal government believes the tax exemption on state and local government debt is a costly subsidy that siphons to investors much of the largesse intended for municipalities.

By shifting more municipal borrowing into the taxable market and tinkering with the subsidy rate, the federal government hopes, as it stated in its budget proposal, to “provide more support to state and local governments than do tax-exempt bonds, but at the same cost to the federal government.”

This statement is not as simple as it sounds. Refashioning the cost and support of the tax exemption in the guise of cash entails guesswork because both the cost of and the support provided by tax-exempt bonds are anything but clear.

A total of roughly $530 billion a year is spent on infrastructure projects like highways, airports, water and energy utilities, garbage disposal sites, schools, and hospitals, according to a joint study conducted last October by the Congressional Budget Office and Joint Committee on ­Taxation.

A bit less than half of this is spent by the private sector, and about an eighth is spent by the federal government itself, either through direct expenditures or through grants.

The remaining $215 billion in infrastructure costs are borne by state and local governments.

Since 1913 — which not coincidentally was when the income tax was enacted — the federal government has indirectly contributed to the municipal share of this spending by exempting interest income on state and local government debt from federal income tax.

This enables municipalities to borrow more cheaply, because investors are willing to accept lower yields on bonds when they are tax-free.

The benefits of this subsidy are the reduction in borrowing costs. The costs are the taxes the federal government does not collect. Washington believes the costs outweigh the benefits.

In its latest budget, the administration estimated it will sacrifice about $38.7 billion in tax revenue next year by excluding the interest on municipal bonds from taxation.

According to estimates cited by the CBO, only about 80% of this — or $31 billion — will actually benefit municipalities. The rest is waste.

In other words, reducing municipalities’ borrowing costs by 80 cents through tax exemption costs the federal government $1.

For example, say a school district wants to borrow $10 million for 30 years. Assume investors in the taxable bond market demand 6% a year from the ­district.

Under basic economic theory, the district’s borrowing costs in the tax-exempt market should be 3.9%, because investors in the 35% tax bracket would view a 6% taxable rate and a 3.9% tax-free rate as essentially the same thing.

If that were all there was to it, nothing would be wasted and this article would already be over.

In a reality divorced from the economic models, it does not happen that way. The reason: with municipalities floating more than $400 billion in bonds a year, there simply are not enough people in the top tax bracket to buy it all. Therefore state and local governments have to appeal to investors in lower tax brackets, too.

After exhausting the 35% tax bracket investors, the school district has to satisfy investors in the 25% tax bracket to find enough buyers for the deal.

That means it needs to offer at least 4.5% interest on the tax-exempt bonds, or else the 25% tax-bracket investors would prefer a 6% taxable rate to the one offered on tax-exempt bonds.

If the 4.5% rate is the one that clears the market, the district must pay that rate to everyone — even the top tax-bracket investors who in this example would have been willing to settle for 3.9%.

Now imagine the school district has borrowed $10 million at a 4.5% tax-exempt interest rate. The district has saved money compared with the 6% it would have paid in the taxable market. But the federal government has overpaid.

Theoretically, investors in the 35% tax bracket would have been willing to buy the bonds at a 3.9% rate — in fact that’s effectively what they would be collecting if they bought the 6% taxable bond. They instead are enjoying a 4.5% rate — free money.

Those extra 0.6 percentage points are dead weight: money the investors would have been willing to pay in taxes that instead is foregone and confers no benefit to the borrower.

Some of the subsidy intended for the municipality went to the bondholder.