Private Stock Recapitalization Cost Basis

I previously invested in my work’s private company stock which was recently recapitalized
with a private equity firm. My original holdings were purchased at a few different share
prices over the years. At the time of the recapitalization I elected to sell/cash out some of
my holdings at a new price and elected to carry over a dollar amount into the newly
recapitalized company’s stock. I understand my cost basis for the shares I sold is the price
I sold at minus the average share purchase price, but how do I come up with the cost basis
for the shares held in the “new” company? I am confused as I elected to rollover a dollar
amount and not a number of shares and the “new” company has a much higher initial
stock price. Any help is appreciated.