In a neighborhood where cash is king, does phasing out pennies really save?

I was shocked to see a credit card terminal appear in Sulmona last year. And I'll never get used to being asked "cash or credit" in Parziale's. So we're headed in a cash-less direction in the North End. But there are still many hold outs that only accept cash in our little corner. How will the Treasury's plan to stop minting pennies play out?

The Treasury plans to stop minting pennies once its current supply of blanks is exhausted. The reason? Each penny actually costs 3.69 cents to make! So it would seem to make money-saving sense to eliminate the cent in cash transactions and round everything to the nearest 5¢.

Will that plan really "save" the Treasury $56 million as they claim?

No. Eliminating pennies will result in more nickels being used and nickels cost 13.78 cents each to make! But how does eliminating pennies result in more nickels being exchanged?

If we simply look at the minimum number of coins to make exact amounts from 1 - 99¢, then the number of nickels involved stays the same. There are 40 exact-price scenarios where one nickel is needed with pennies and 40 exact-price scenarios where one nickel is needed when prices are rounded to the nearest 5¢. But when we look at businesses making change for purchases that customers make using whole dollars, there is an interesting phenomenon with certain prices such as those nearing one whole dollar.

Take an item that costs $1.97:
With a customer paying $2, the business would provide three pennies in change. Without pennies, the business would round down to $1.95 and give a nickel in change. In the first (penny) scenario, the original minting of the three pennies represent 8.07 cents in excess costs. In the second (penny-less) scenario, the single nickel represents 8.78 cents in excess costs - ~9% in added excess costs to the mint.

Paywalled (NYTimes) article with more in depth analysis including the possiblity of phasing out the nickel:
So, You Want to Get Rid of the Penny. Do You Have a Plan for the Nickel?