To estimate a maximum purchase price for the coin in question, we can analyze several factors:

1. Starting Price: 150 euros.
2. Auction History: The coin has been auctioned 15 times, of which it has sold 13 times. This indicates good demand.
3. Average Hammer Price: 109.85 euros, which is a good indicator of the coin's real market value.
4. Previous Prices:
- In 2023, it was auctioned with a starting price of 120 euros and hammered down at 270 euros, indicating potential for a high hammer price.
- In other auctions, hammer prices have varied, but there are examples of hammer prices exceeding the starting price.

5. Condition: There is no specific information about the condition of this coin, which may make its value more uncertain. However, the price history shows that it has reached high values in the past.

Given that the starting price is 150 euros and considering the hammer price history, an estimated maximum purchase price could be positioned in a range between the average hammer price and the highest recorded hammer price.

Estimated Maximum Purchase Price: It may be reasonable to consider a maximum purchase price of around 250-300 euros, given the observed hammer price potential in previous auctions and the demand that the coin seems to have. This is based on the fact that it has reached hammer prices of up to 270 euros in the past.