The way they handle the public’s money, sometimes we wonder how it is that most Manchester aldermen are not bankrupt and homeless.

Last month, aldermen voted over Mayor Ted Gatsas’ strong objections to accept federal grants to fund new police and firefighter positions.

The firefighter money comes from the Department of Homeland Security’s SAFER program. It would fund eight firefighters through 2014. The city would be required by the terms of the grant to pay the full costs of employing all eight firefighters in 2015, a figure estimated to be $600,000.

The police funding comes through the federal Community Oriented Policing (COPS) program. It would pay for five new officers. The city would have to pay roughly $18,000 in 2013, $50,000 in 2014, $50,000 in 2015 and $233,000 in 2016, city Finance Director Bill Sanders has calculated.

The aldermen called this a great deal. It might be if those positions were essential and the city had the means to fund all of them not just in those final years, but in perpetuity. It does not.

The fallacy behind these grants, a fallacy warmly embraced by a majority of aldermen, is that the federal money provides the city with needed personnel for free.

Anyone who has joined a mail-order book or music club should realize the flaw immediately. The “free” goodies given up front cost you much more in the long run because they obligate you to spend money you would not otherwise have spent.

Though these grants require only a one-year committment on the part of the city, the reality is that public employee unions and their political allies make it difficult to lay off police officers and firefighters. The odds are that the aldermen will not let these new hires go, and the taxpayers will have to fund them forever.

Again, that might be defensible if the city were flush with cash. But the city pink slips teachers every year for want of ready cash to continue funding even its existing obligations. The fact is that these hires put great pressure on the city to raise taxes.

Other municipalities are more responsible. “I have not applied for a COPS grant for a while because of the requirements,” Derry Police Chief Edward Garone told our correspondent, Barbara Taormina, earlier this month. “Derry, like every other community, is facing some serious budget issues.”

Manchester is, too — in part because a majority of the aldermen keeps obligating the city to spend more than it has coming in.