Assume that you own 4000 shares of Omicron stock and that Omicron uses the entire $50 million to ...

What you have:

Enterprise Value = PV(Future FCF) =   = $400 million
Market value = Enterprise Value + cash = $400 + $50 = $450 million

Share price =   =   = $45.00 × 4000 shares = $180,000 of stock.

What you want:

Enterprise Value - PV(Future FCF) =   = $400 million
Market value = Enterprise Value + cash = $400 + $50 = $450 million

However, once the $50 million in cash is used to pay the dividend, the new market value becomes $450 - $50 = $400 Million

Share price =   =   = $40.00 × 4000 shares = $160,000 of stock

Dividends that you want to receive = 4000 shares × $5 share = $20,000 cash

What you need to do:

You have $180,000 in stock and want $160,000 in stock and $20,000 in cash, so you must sell $20,000 worth of stock.  To accomplish this:

Number of shares to sell =   = 444.44 shares

So by selling 444.44 shares you obtain the desired results.