Negotiating salary with Pr

I just got a call from a PE firm that I was in discussion with for a Director role. The firm came back and offered very low comp (average comp for a VP role). I countered and said that it was low based on comparable sales put together by Headhunters + I make more at current role. They say it will be very hard for them to match it because it’s a new fund and that more will come later. Is this typical for PE firms to try to low ball you? It’s about $1B AUM firm