Londonrocks

the value of the option at exipiration is not 114. 114 is just an hypothetical price at expiration. is like looking forward moving back.

if 114 is the breakeven price, what does that imply about the price of the put at the time of purchasse. this can be translate into X-St-P=0 where P is the price of the option.

Now remember the value of the put at the time of purchase is not zero because, we do not know at that time that the price at expiration would be 114. the question clearly says IF.... the price is 114. so it is just an hypothesis to find the breakeven price today based on an hypothetical price of the asset at expiration.