Dividends tax effect on DCF

Guys, I don't understand why DCF is not affected by dividends tax.

Let's assume that dividend tax goes from 0% to 15%. FCFE is not going to change, what is the rational behind it? I guess that since shareholders are going to receive less dividends, the company's value should reduce somehow cause investor are less willing to pay for it.

I thought that maybe cost of equity might increase to compensate the tax effect and this would reduce FCFE. But I didn't find anything about that.

I hope someone can help me to find this out. Thanks!