To estimate a maximum purchase price for the coin that is going to be auctioned, we can consider several factors based on the provided data:

1. Starting price: 90 euros.
2. Average hammer price in previous auctions: 126 euros.
3. Auction history: The coin has been auctioned 18 times, of which it has sold 14 times. This indicates good demand.
4. Previous hammer prices: The hammer prices have varied, but there are several cases where the hammer price has been above 120 euros.
5. Condition: There is no information about the condition of the coin, which may make the price more uncertain.

Given that the average hammer price is 126 euros and considering that the starting price is 90 euros, an estimated maximum purchase price could be in a range between the average hammer price and a bit more, given the auction history.

Taking all these factors into account, an estimated maximum purchase price could be approximately 150 euros. This is based on the average hammer price and the fact that in some previous auctions, hammer prices have reached up to 160 euros.