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

1. Current Condition: The coin has a condition of 100 (MS), indicating that it is in excellent shape. This generally translates to a higher price compared to coins with lower conditions.

2. Auction History:
- The average hammer price for similar coins in the past is 89.87 euros.
- The coin has been auctioned 16 times, of which it has sold 15 times, indicating good demand.
- In previous auctions, hammer prices have varied significantly, with some reaching up to 160 euros for a condition of 100.

3. Starting Price: The current starting price is 125 euros, which is higher than the average starting price of 50.19 euros. This suggests that the seller has high expectations due to the coin's condition.

4. Comparison with Previous Prices:
- In the 2019 auction, a coin with a condition of 100 sold for 160 euros.
- In other auctions, hammer prices have ranged from 28 to 160 euros, depending on the condition.

Given that the coin has a condition of 100 and considering the hammer price history, an estimated maximum purchase price could be between 150 and 180 euros. This is based on the fact that the highest hammer price in the past for a coin of similar condition was 160 euros, and since the current condition is excellent, it is reasonable to expect that the hammer price could be in the upper range.

Therefore, an estimated maximum purchase price could be approximately 170 euros.