To estimate a maximum purchase price for the coin that will be auctioned, we will consider several factors:

1. Condition: The coin in question has a condition rating of 110 (FDC), indicating that it is in exceptional condition. This generally increases its value compared to coins of lower condition.

2. Starting Price: The starting price is 90 euros. This is the starting point for the auction.

3. Auction History:
- The coin has been auctioned 13 times in the past, of which it has sold 11 times. This indicates good demand.
- Previous hammer prices for coins of similar condition (95 and 90) have varied, but the highest recorded price is 50 euros in a previous auction, although this may not be representative due to the condition.

4. Price Trends: The average hammer price in previous auctions is 19.09 euros, but this includes coins of lower condition. For coins in FDC condition, a significantly higher price can be expected.

5. Previous Price Estimates: In past auctions, estimated prices for coins of similar condition have been up to 40 euros, but with the FDC condition, it is reasonable to expect the hammer price to be considerably higher.

Given all this, an estimated maximum purchase price could be between 150 and 200 euros, considering the high condition and historical demand. However, the starting price of 90 euros suggests that there could be a good buying opportunity if competition is not high.

Therefore, a reasonable maximum purchase price could be 150 euros.