Cash out / cash in - how to treat?

Question which I am pretty sure I have right but want to reconfirm / understand if there is any grey zone.

Company has 5,000 shares and agrees to a cash out / cash in deal with a PE fund @ an equity valuation of $20m cash in / $15m cash out

$1m cash in and $1m cash out.

Is the order of this transaction as following?:

1. PE fund acquires 333 shares @ $3000 a share

2. 250 new shares issued which fund acquires @ $4000 per share

New shareholding:

Principals - 4,667 shares (88.9%)

PE fund - 583 shares (11.1%)

Total shares = 5,250

The point thats throwing me off is would the cash out shares be purchased after new shares are issued or before? / is this traditionally a point of negotiation with the PE firm

Many thanks in advance!