Increasing growth rate of dividends - effect on Index price

Excuse the silly question but I always thought that dividends lowered the price of the stock. Here is the question:

If the expected growth rate in dividends for large capitalization stocks increases by 60 basis points, which of the following would benefit the most? An investment in: a. long futures on the S&P 500 index b. short futures on the S&P 500 index c. long put options on the S&P 500 index The answer says that the long futures on the S&P 500 index will increase in value due to the increased growth rate in dividends for large cap stocks. So the answer given is a. One way to look at it is that using the constant growth model clearly the value of the company in question will increase if the dividend rate is increasing. Understandably this would cause the value of the Index in which this is a constituent to increase. On the flip side, you can argue that the moment a dividend is paid by a firm, that firm’s stock price decreases by the amount of the dividend. I’m pretty sure that stock indices such as the S&P 500 pay dividends, so wouldn’t the value that a particular stock contributes to the index decrease, thus decreasing the value of the index? Can someone please correct my train of thought? Just to be absolutely clear, the answer provided is A.

The stock price falls by the price of the dividend because an asset that the company had is relinquished to equity holders. $100m to investors with 100m shares, and each share is now worth $1 less since owning a share doesn’t give you an ownership stake in the company’s cash anymore (instead, they put the cash right into your pocket). The company DID NOT change their expected dividend growth rate, though. The stock price simply decreased due to the planned dividend payout.

Now take a company with a particular growth rate of dividends, and increase it, all else equal. The nominal value of their dividends is higher every period, and therefore so is the present value of their stream of dividend payments. The company is now worth more, so its stock price increases. Its dividend is also higher, so when it does pay out a dividend, the share price decreases by more than it otherwise would have. However, this effect is negligible compared to the increased share price from the new valuation.

Large cap stocks are able to pay high dividends when they make a lot of money, and they tend to be worth more when they make a lot of money compared to no money.