Update 12-26-2013:

Update 10-16-2013:

This means the added cost of the signs will be the cost of paint, metal, and power for the extra size of the signs over the Cantrell signs which were already scheduled to be replaced to meet readability standards.

The sound bite:

The finance:

The initial figure of $26,500 is consistent with a full expensing of all costs related to the relevant department allocated over the portion of the year's activity represented by putting up the signs. When Drew Williams says "The Public Works Department covers costs associated with sign upkeep in its annual maintenance budget" that means they are expensing not only the signs themselves but the cost of the workers, who would be on the payroll regardless of the street naming, the cost of their trucks, and even the cost of the buildings in which the trucks are stored. In managerial accounting, this is called expensing overhead costs. It is a completely different concept than the extra cost for changing the street name. Even this extra cost is not a new cost to the tax payers, but rather already a budget item in a city budget that has wiggle room built in for unexpected expenses on the scale of three million dollars, based on the most recent budget hearings.

Here are a pair of key quotes from the above linked article by Preston Knight that amounts to a principled retraction of his article from the previous day that joined WHSV in claiming $26,000:

"For Harrisonburg, the regulations [on "retroreflectivity" which mean
all city signs are in the process of being replaced] mean the cost
associated with changing Cantrell to Martin Luther King Jr. Way is not
necessarily an entirely new expense, just earlier than planned."
...
"Even without a name change, though, the city would have had to buy new
signs and pay for labor to replace current Cantrell signs to comply
with regulations at some point. The Public Works Department covers
costs associated with sign upkeep in its annual maintenance budget,
Assistant Director Drew Williams said."

The General fund for this year was $115,083,113. The total funds
for this year were $282,678,454.  1.3 million dollars were budgeted
for information technology, much no doubt on licenses for things that
could have been done as well or better with free software.  To give
the people smaller numbers to chew on, $531,844 was budgeted for
street lights. $276,192 was budgeted for street beautification.  Yes,
this historic decision will cost only 1/10=10 percent of what we spent
this year simply to beautify our streets.

One tenth the price of street beautification, to show bigots don't
rule this city and to let the world know to look here for more than
just the history of Confederates who fought, killed, and died to
preserve slavery and the feudal society built upon it, and the history
of segregationists who massively resisted its demise for another
century after the Civil War.

And-  did the city manager say in his figures that those city
employees, accounting for up to nine tenths (90 percent) of the
cost,  would be furloughed if we did not do the Martin Luther 
King renaming, thus saving the city 20 some thousand dollars? 
NO. They would have been doing something else. So, some signs 
that need replacing might go another year or two and yellow 
a bit because the Cantrell signs were moved ahead in line.  

Are the people who shout about this, and who report it out of 
context, racist, innumerate, both, or something else?

$26,000- all in a day's work.

As the parts of the budget referenced in the city estimate started to come out in a WSHV report that mentioned the cost had already been included in the budget, one commenter repeated the theory that has made the rounds elsewhere, that the street renaming was decided in advance.

What was decided in advance was that our friendly city would have safe, beautiful, well maintained streets and that we would use our taxes to sustain a team of full time professionals with quality equipment to get the job done. In the normal course of one day's street maintenance, we had them put one name rather than another on a group of old signs that they were already about 1/3 of the way into replacing anyway.