With $S_0=100$ and $T=8$. Looking at the payoff it seems obvious that it is replicated with two european put options ($K=100$ and $K=150$) and an european call option ($K=200$), therefore:
And hence the initial value needed to replicate the derivative is $V_0=50$. However, in the solution of the problem it says that the initial value is 41.4. Where am I wrong?