Here's the deal. Let's say Perk would get a four- or five-year contract on the free agent market. One, there are a lot of teams who are willing to overpay; just look at the number of bad contracts that teams try to move, including guys who were signed to lucrative deals this off-season. Two, these teams are willing to overpay on top of an optimistic assumption that Perkins will be mostly healthy for the duration of the contract.
Danny Ainge does not like to lock up injury-prone players to long-term deals. That's why Leon Powe was not in his long-term plans. That's why he didn't want to give Tony Allen a guaranteed third year. I think it is one reason why he decided Jermaine O'Neal for two years was a better MLE gamble than Brad Miller for three years.
Ainge, if he follows past behavior, would have wanted a discount, either in fewer dollars committed or in unguaranteed money on the end of a contract. Possibly, Perkins signaled that he wanted to maximize his money on the free agent market, but would give the Celtics a chance to match.
Anyone who wants to pay (or even overpay) Perk based on expected value under the assumption that he will be healthy for the duration of the contract is a horrible armchair GM who might not even be as competent as Chris Wallace.