Exercising an American call option early

I have seen the rationale behind why it is never optimal to exercise an American call option early, but have a question about it.

If the option strike price is $E=\$20$ and it expires at $T=1yr$, if the share price is $S=\$25$ at expiry, the profit will be $\$5$ per share. However, what if at $T=0.5yr$ the share price was $S=\$40$ following a jump in the price. Exercising at this point would yield a profit of $\$20$ per share.

Would it not be more optimal to exercise early, in this case?