One roster spot and $443,106 in payroll. This also increases the team's cap space from $1,413,034 to $1,856,140. So they got that going for them, which is nice. (Salary data from ShamSports.com)
The most the Hawks can offer a free agent is the Room Mid-Level Exception which is worth a starting salary of $2,652,000 as of right now. But once January 10th hits, then this value starts to decrease in value by 1/170th each day. (170 is based on number of days in the NBA season, calculated below).
The Hawks still have the option of signing someone with their cap space and then using the Room Mid-Level Exception.
If the Hawks did not waive Cartier Martin by today at 5:00PM, then Cartier Martin's minimum salaried deal would be guaranteed. A minimum salaried contract for a player with 5 years experience is worth $1,027,424. A nifty trick in the CBA is that an NBA team is only billed up to the minimum salary for a player with 2 years experience ($884,293) and any amount paid in excess is covered by the league. This is a benefit that the NBA Players Association was able to negotiate for minimum salaried players with 3 or more years experience.
When calculating the amount owed to a player, the timing of the release is important. Players are not paid by game, but rather they are paid in relation to number of days spent on a roster out of the total number of days in the NBA Season. This season started on October 29th and ends April 16th, which puts the season at a cool 170 days. Since today is January 7th, Cartier was on the Hawks roster for 71 days (edit: but he has 48 hours to clear waivers and so the Hawks will pay him for 73 days; numbers have been corrected). This means that Cartier was paid [(73/170)*$1,027,424 =] $441,188 for his services this year. The Hawks will be charged this same amount towards their Team Salary.
If the Hawks did not waive Cartier Martin, then that would have guaranteed Cartier $586,237 for the rest of the season. Of that amount, the Hawks would have been responsible for $443,106 and the NBA would have picked up the rest of the $143,131.
Is the roster spot a big issue? No, not really. The Hawks could have still waived Cartier at a later date. However, that scenario would have cost the Hawks $443,106. So it is not the roster spot that is of value but that strange thing called money that is of value here.
Can the Hawks resign Cartier? Sure. They can sign him to a Rest-of-Season contract (would be guaranteed) or up two 10-day contracts (with the ability to still sign him to a Rest-of-Season contract). The same stipulations as before apply, the Hawks will only be responsible for up to the minimum salary of a player with 2 years experience. So hang in there Cartier, Danny may be in touch with you!