In your example, I believe it's assumed that the exercise date is after the dividend date. If the dividend date is after the exercise date, nothing happens. The value would decrease, consider the following timeline:
- $t=0$: You have a call option worth $4.73$ and a stock worth $S_0$
- $t=1$: The increase in dividend is announced but dividends are not paid out yet.
- $t=1 + \varepsilon$: The price of the option changes.
- $t=2$: The dividend is paid.
- $t=3$: Expiration date.
At $t=2$, the price of the stock would decrease by $.37$ more than was expected at $t=0$. This implies a downward adjustment of the option price at $t=3$ and one can expect that the price of the option from $t=1$ to $t=1+\varepsilon$ to decrease. It's less likely to end in the money and if it ends in the money the payoff would be lower, ceteris paribus.
Dividend decisions don't change company value as a first order effect. A decision to change dividends might give a signal to the market which has an effect on the price but the size and sign of that signal are hard to determine in general. Dividends come from the assets of the company so a dividend decrease the company value by the amount that is paid out. Otherwise it would be free lunch.